Android : Refreshing listview adds duplicates

I'm using a swipe-down to refresh implementation that calls this on refresh:

public void onRefresh() {
        swipeLayout.setRefreshing(true);
        swipeLayout.setColorScheme(android.R.color.holo_blue_dark, android.R.color.holo_blue_light, android.R.color.holo_green_light, android.R.color.holo_green_light);
        (new Handler()).postDelayed(new Runnable() {
            @Override
            public void run() {
                swipeLayout.setRefreshing(false);
                Toast.makeText(getApplicationContext(), "The refresh is working!", Toast.LENGTH_SHORT).show();
                AppController.getInstance().getRequestQueue().getCache().remove(URL_FEED);
                feedRequest();

            }
        }, 2000);
    }

It invalidates the cache and makes a fresh call to the server with Volley (feedRequest).

Here's how I parse the response from that data to be displayed:

private void parseJsonFeed(JSONArray response) {
        try {

            for (int i = 0; i < response.length(); i++) {
                JSONObject feedObj = (JSONObject) response.get(i);

                FeedItem item = new FeedItem();
                item.setId(feedObj.getInt("id"));

                item.setHeadline(feedObj.getString("headline"));

                item.setTimeStamp(feedObj.getString("created_at"));

                JSONObject mVendor = feedObj.getJSONObject("vendor");
                item.setVendorPic(mVendor.getString("image_url"));

                item.setImge(feedObj.getString("image_url"));

                feedItems.add(item);
            }

            listAdapter.notifyDataSetChanged();
        } catch (JSONException e) {
            e.printStackTrace();
        }
    }

So when I call notifyDSC it adds all of the parsed items into the existing list, including items that might already exist in the list. How can I ensure that I don't end up with duplicates? I thought about wiping the List clean in onRefresh(), but that doesn't seem optimal unless I have to do that. Any ideas on how to solve this problem?