diff --git a/package/CHANGELOG b/package/CHANGELOG
index 133cfe3ea92..b53ffc987bf 100644
--- a/package/CHANGELOG
+++ b/package/CHANGELOG
@@ -21,6 +21,8 @@ The rules for this file:
  * 2.8.0
 
 Fixes
+ * Fix `MDAnalysis.analysis.align.AlignTraj` not accepting writer kwargs
+   (Issue #4564, PR #4565)
  * Fix #4259 via removing argument `parallelizable` of `NoJump` transformation.
  * Fix doctest errors of analysis/pca.py related to rounding issues 
    (Issue #3925, PR #4377)
diff --git a/package/MDAnalysis/analysis/align.py b/package/MDAnalysis/analysis/align.py
index dd0e0100e64..2bc80042b69 100644
--- a/package/MDAnalysis/analysis/align.py
+++ b/package/MDAnalysis/analysis/align.py
@@ -681,6 +681,7 @@ class AlignTraj(AnalysisBase):
     def __init__(self, mobile, reference, select='all', filename=None,
                  prefix='rmsfit_', weights=None,
                  tol_mass=0.1, match_atoms=True, strict=False, force=True, in_memory=False,
+                 writer_kwargs=None,
                  **kwargs):
         """Parameters
         ----------
@@ -720,6 +721,8 @@ def __init__(self, mobile, reference, select='all', filename=None,
         verbose : bool (optional)
              Set logger to show more information and show detailed progress of
              the calculation if set to ``True``; the default is ``False``.
+        writer_kwargs : dict (optional)
+            kwarg dict to be passed to the constructed writer
 
 
         Attributes
@@ -780,6 +783,9 @@ def __init__(self, mobile, reference, select='all', filename=None,
            :attr:`rmsd` results are now stored in a
            :class:`MDAnalysis.analysis.base.Results` instance.
 
+        .. versionchanged:: 2.8.0
+           Added ``writer_kwargs`` kwarg dict to pass to the writer
+
         """
         select = rms.process_selection(select)
         self.ref_atoms = reference.select_atoms(*select['reference'])
@@ -816,10 +822,12 @@ def __init__(self, mobile, reference, select='all', filename=None,
             self.ref_atoms, self.mobile_atoms, tol_mass=tol_mass,
             strict=strict, match_atoms=match_atoms)
 
+        if writer_kwargs is None:
+            writer_kwargs = {}
         # with self.filename == None (in_memory), the NullWriter is chosen
         # (which just ignores input) and so only the in_memory trajectory is
         # retained
-        self._writer = mda.Writer(self.filename, natoms)
+        self._writer = mda.Writer(self.filename, natoms, **writer_kwargs)
 
         self._weights = get_weights(self.ref_atoms, weights)
 
@@ -1661,4 +1669,4 @@ def get_atoms_byres(g, match_mask=np.logical_not(mismatch_mask)):
                 logger.error(errmsg)
                 raise SelectionError(errmsg)
 
-    return ag1, ag2
+    return ag1, ag2
\ No newline at end of file
diff --git a/testsuite/MDAnalysisTests/analysis/test_align.py b/testsuite/MDAnalysisTests/analysis/test_align.py
index 78ba028a114..63dfd25db80 100644
--- a/testsuite/MDAnalysisTests/analysis/test_align.py
+++ b/testsuite/MDAnalysisTests/analysis/test_align.py
@@ -353,6 +353,17 @@ def test_AlignTraj_in_memory(self, universe, reference, tmpdir):
         self._assert_rmsd(reference, universe, 0, 6.929083044751061)
         self._assert_rmsd(reference, universe, -1, 0.0)
 
+    def test_AlignTraj_writer_kwargs(self, universe, reference, tmpdir):
+        # Issue 4564
+        writer_kwargs = dict(precision=2)
+        with tmpdir.as_cwd():
+            aligner = align.AlignTraj(universe, reference,
+                                      select='protein and name CA',
+                                      filename='aligned_traj.xtc',
+                                      writer_kwargs=writer_kwargs,
+                                      in_memory=False).run()
+            assert_equal(aligner._writer.precision, 2)
+
     def _assert_rmsd(self, reference, fitted, frame, desired, weights=None):
         fitted.trajectory[frame]
         rmsd = rms.rmsd(reference.atoms.positions, fitted.atoms.positions,