Recently, automated neural network architecture design (neural architecture search) has yielded many significant achievements. Improving the prediction accuracy of the neural network is the primary goal. However, besides the prediction accuracy, other types of cost including memory consumption, inference time, and training time are also very important when implementing the neural network. In practice, such types of cost are often bounded by thresholds. Current neural architecture search method with budgeted cost constraints can only optimize some specific types of the cost. In this paper, we propose budgeted efficient neural architecture search (B-ENAS) to optimize more types of cost. The experimental results on the well-adopted CIFAR10 dataset show that B-ENAS can learn convolutional neural network architectures with high accuracy under different cost constraints.