If you want to use google autocomplete api on modal popup. when you are getting data through ajax on modal pop. then you can use below code :

1. your ajax code :

$.ajax({ 
		data: {YOUR_DATA},
		type: 'post',
			url: 'YOUR_AJAX_URL' ,
			success: function(response) {
			if (response) {
				var json_array = $.parseJSON(response);
				if(json_array['status']=='success'){
				$('#YOUR_MODAL_ID').modal('show');
					showSuggestionMap();
					google.maps.event.addDomListener(window, 'load', showSuggestionMap);
				}	
			}
		}
	}); 

2. after this use below script function :

function showSuggestionMap() {
		var input = document.getElementById('YOUR_INPUT_FIELD');
		var options = { componentRestrictions: {country: 'au'} };
		var autocomplete = new google.maps.places.Autocomplete(input, options);
		google.maps.event.addListener(autocomplete, 'place_changed', function() {
		var place = autocomplete.getPlace();
		});
		var input = document.getElementById('YOUR_INPUT_FIELD');
		google.maps.event.addDomListener(input, 'keydown', function(event) { 
			
		});
	}

3. use below css :

.pac-container .pac-logo { z-index:9999999;}

Output :