In shared preferences how to store string array in android application

You can try using JSONArray as JSON is light-weight also, you can create a JSONArray and write it to SharedPreference as String.

To write,

       SharedPreferences prefs = PreferenceManager
                .getDefaultSharedPreferences(this);
        JSONArray jsonArray = new JSONArray();
        jsonArray.put(1);
        jsonArray.put(2);
        Editor editor = prefs.edit();
        editor.putString("key", jsonArray.toString());
        System.out.println(jsonArray.toString());
        editor.commit();

To Read,

        try {
            JSONArray jsonArray2 = new JSONArray(prefs.getString("key", "[]"));
            for (int i = 0; i < jsonArray2.length(); i++) {
                 Log.d("your JSON Array", jsonArray2.getInt(i)+"");
            }
        } catch (Exception e) {
            e.printStackTrace();
        }

If you are using API 11 then its possible by using putStringSet. Otherwise you may either convert your string array into a single string as mentioned by @hotverispicy or use SQLite database

you can save it as string by ,(comma) seperator and while fetching just use split()

string toPut="";

toPut += "listItem,";

set toPut in your SharePreference and commit()

To get the same in array: get prefString from SharePreference

String[] fetchArray= prefString.split(",");