diff --git a/etc/ORG-NEWS b/etc/ORG-NEWS
index a4725ae8c..d75efdeda 100644
--- a/etc/ORG-NEWS
+++ b/etc/ORG-NEWS
@@ -13,6 +13,21 @@ Please send Org bug reports to mailto:emacs-orgmode@gnu.org.
 
 * Version 9.7 (not released yet)
 ** Important announcements and breaking changes
+*** ~org-store-link~ now moves an already stored link to front of the ~org-stored-links~
+
+Previously, when the link to be stored were stored already,
+~org-store-link~ displayed a message and did nothing.
+
+Now, ~org-store-link~ moves the stored link to front of the list of
+stored links.  This way, the link will show up first in the completion
+and when inserting all the stored links with ~org-insert-all-links~.
+
+The new behavior is controlled by new customization ~org-link-store-existing~.
+
+Users can set ~org-link-store-existing~ to nil to revert previous
+defaults.  The value of =store-duplicate= will force duplicate links
+in ~org-stored-links~.  The default value is =move-to-front=.
+
 *** Major changes and additions to Org API
 **** New term: "syntax node"
 
diff --git a/lisp/ol.el b/lisp/ol.el
index 6dd7e0fa1..3a8ca5f39 100644
--- a/lisp/ol.el
+++ b/lisp/ol.el
@@ -509,6 +509,20 @@ links more efficient."
   :type 'boolean
   :safe #'booleanp)
 
+(defcustom org-link-store-existing 'move-to-front
+  "Variable controlling how to deal with already stored links.
+When nil, ignore store request for an already stored link.
+When symbol `move-to-front', move the stored link to the front of
+`org-stored-links'.
+When symbol `store-duplicate', add a duplicate in front."
+  :group 'org-link-store
+  :type '(choice
+          (const :tag "Do no store duplicate" nil)
+          (const :tag "Move stored duplicate to front" move-to-front)
+          (const :tag "Store duplicate" store-duplicate))
+  :safe #'symbolp
+  :package-version '(Org . "9.7"))
+
 ;;; Public variables
 
 (defconst org-target-regexp (let ((border "[^<>\n\r \t]"))
@@ -1749,16 +1763,24 @@ non-nil."
       ;; Store and return the link
       (if (not (and interactive? link))
 	  (or agenda-link (and link (org-link-make-string link desc)))
-	(if (member (list link desc) org-stored-links)
-	    (message "This link has already been stored")
-	  (push (list link desc) org-stored-links)
-	  (message "Stored: %s" (or desc link))
+        (dotimes (_ (if custom-id 2 1)) ; Store 2 links when CUSTOM-ID is non-nil.
+          (pcase org-link-store-existing
+            ((or `store-duplicate
+                 (guard (not (member (list link desc) org-stored-links))))
+             (push (list link desc) org-stored-links)
+	     (message "Stored: %s" (or desc link)))
+            ((or`nil (guard (equal (list link desc) (car org-stored-links))))
+             (message "This link has already been stored"))
+            (`move-to-front
+             (setq org-stored-links
+                   (delete (list link desc) org-stored-links))
+             (push (list link desc) org-stored-links)
+             (message "Link moved to front: %s" (or desc link))))
 	  (when custom-id
 	    (setq link (concat "file:"
 			       (abbreviate-file-name
-				(buffer-file-name (buffer-base-buffer)))
-			       "::#" custom-id))
-	    (push (list link desc) org-stored-links)))
+			        (buffer-file-name (buffer-base-buffer)))
+			       "::#" custom-id))))
 	(car org-stored-links)))))
 
 ;;;###autoload