ListView with searching feature is very common in applications. You just need an EditText at the top of the ListView or as per your designs.
Below are the steps-

First you need to initialize the ListView and EditText

countryCodelistView = (ListView) findViewById(R.id.country_code_list_view);
countryCodeSearchEditText = (EditText) findViewById(R.id.country_code_search);

Now add ArrayAdapter in a ListView

adapter = new ArrayAdapter<String>(this, R.layout.country_code_list_item,
                R.id.country_code_text_view, array);
countryCodelistView.setAdapter(adapter);

Here array is the list that holds by a ListView

Now final step is to apply addTextChangedListener on the EditText

countryCodeSearchEditText.addTextChangedListener(new TextWatcher() {

            @Override
            public void onTextChanged(CharSequence cs, int arg1, int arg2,
                    int arg3) {
                // When user changed the Text
                CountryCodeActivity.this.adapter.getFilter().filter(cs);
            }

            @Override
            public void beforeTextChanged(CharSequence arg0, int arg1,
                    int arg2, int arg3) {
                // TODO Auto-generated method stub

            }

            @Override
            public void afterTextChanged(Editable arg0) {
                // TODO Auto-generated method stub
            }
        });