<div ng-app="myApp" ng-controller="myCtrl">
  <select ng-model="selectedOption" ng-options="option for option in options">
    <option value="">自定义</option>
  </select>
  <input type="text" ng-model="customOption" ng-show="selectedOption === ''">
</div>

var app = angular.module('myApp', []);
app.controller('myCtrl', function($scope) {
  $scope.options = ['选项1', '选项2', '选项3'];
  $scope.selectedOption = '';
  $scope.customOption = '';

  $scope.$watch('selectedOption', function(newValue) {
    if (newValue === '') {
      $scope.customOption = '';
    }
  });
});