diff --git a/doc/org-manual.org b/doc/org-manual.org
index 5f55e9bd5..3758d8cd4 100644
--- a/doc/org-manual.org
+++ b/doc/org-manual.org
@@ -6337,6 +6337,10 @@ special repeaters =++= and =.+=.  For example:
 ,** TODO Check the batteries in the smoke detectors
    DEADLINE: <2005-11-01 Tue .+1m>
    Marking this DONE will shift the date to one month after today.
+
+,** TODO Wash my hands
+   DEADLINE: <2019-04-05 08:00 Sun .+1h>
+   Marking this DONE shifts the date to exactly one hour from now.
 #+end_example
 
 #+vindex: org-agenda-skip-scheduled-if-deadline-is-shown
diff --git a/etc/ORG-NEWS b/etc/ORG-NEWS
index 2b60f2939..e90ac60e3 100644
--- a/etc/ORG-NEWS
+++ b/etc/ORG-NEWS
@@ -353,6 +353,17 @@ to the resulting HTML file.
 
 Org refile variables and functions have been moved to a new file.
 
+*** Handle repeated tasks with =.+= type and hours step
+
+A task using a =.+= repeater and hours step is repeated starting from
+now. E.g.,
+
+#+begin_example
+,,** TODO Wash my hands
+   DEADLINE: <2019-04-05 08:00 Sun .+1h>
+   Marking this DONE shifts the date to exactly one hour from now.
+#+end_example
+
 *** The end of a 7 years old bug
 
 This bug [[https://lists.gnu.org/archive/html/emacs-orgmode/2013-08/msg00072.html][originally reported]] by Matt Lundin and investigated by Andrew
diff --git a/lisp/org.el b/lisp/org.el
index 06891b8bd..57682fd16 100644
--- a/lisp/org.el
+++ b/lisp/org.el
@@ -10146,9 +10146,13 @@ This function is run automatically after each state change to a DONE state."
 			(repeater-type (match-string 1 ts)))
 		    (cond
 		     ((equal "." repeater-type)
-		      ;; Shift starting date to today.
-		      (org-timestamp-change (- (org-today) (time-to-days time))
-					    'day))
+		      ;; Shift starting date to today, or now if
+		      ;; repeater is by hours.
+		      (if (equal what "h")
+			  (org-timestamp-change
+			   (floor (- (org-time-stamp-to-now ts t)) 60) 'minute)
+			(org-timestamp-change
+			 (- (org-today) (time-to-days time)) 'day)))
 		     ((equal "+" repeater-type)
 		      (let ((nshiftmax 10)
 			    (nshift 0))
diff --git a/testing/lisp/test-org.el b/testing/lisp/test-org.el
index dc4a6a59f..6751610a4 100644
--- a/testing/lisp/test-org.el
+++ b/testing/lisp/test-org.el
@@ -6686,6 +6686,28 @@ Paragraph<point>"
      (org-test-with-temp-text "* TODO H\n<2012-03-29 Thu +2h>"
        (org-todo "DONE")
        (buffer-string))))
+  ;; Handle every repeater type using hours step.
+  (should
+   (string-match-p
+    "2014-03-04 .* 02:00"
+    (org-test-at-time "<2014-03-04 02:35>"
+      (org-test-with-temp-text "* TODO H\n<2014-03-03 18:00 +8h>"
+	(org-todo "DONE")
+	(buffer-string)))))
+  (should
+   (string-match-p
+    "2014-03-04 .* 10:00"
+    (org-test-at-time "<2014-03-04 02:35>"
+      (org-test-with-temp-text "* TODO H\n<2014-03-03 18:00 ++8h>"
+	(org-todo "DONE")
+	(buffer-string)))))
+  (should
+   (string-match-p
+    "2014-03-04 .* 10:35"
+    (org-test-at-time "<2014-03-04 02:35>"
+      (org-test-with-temp-text "* TODO H\n<2014-03-03 18:00 .+8h>"
+	(org-todo "DONE")
+	(buffer-string)))))
   ;; Do not repeat inactive time stamps with a repeater.
   (should-not
    (string-match-p