AutoComplete.php

//Controller Action

public function find() {
      
        if ($this->request->is('ajax')) {
            
            $this->autoRender = false;            
            $country_name = $this->request->query('term');            
            $results = $this->Country->find('all', array(
                                           'conditions' => array('Country.name LIKE ' => '%' . $country_name . '%')
                                           'recursive'  => -1
                                           ));
            
            $resultArr = array();
            foreach($results as $result) {
               $resultArr[] = array('label' =>$result['Country']['name'] , 'value' => $result['Country']['name'] );
            }
            echo json_encode($resultArr);                                   
       } 
       
    }

// View and Jquery Code

<?php
echo $this->Form->create('Country', array('action' => 'find'));
echo $this->Form->input('name',array('id' => 'Autocomplete'));
echo $this->Form->submit();
echo $this->Form->end();
?>

<script type="text/javascript">
    $(document).ready(function($){
    $('#Autocomplete').autocomplete({
	source:'<?php echo $this->Html->url(array("controller" => "countries","action"=> "find")); ?>',
	minLength: 2
    });
});
    </script>