Though recent advanced convolutional neural networks (CNNs) have been improving the image recognition accuracy, the models are getting more complex and time-consuming. For real-world applications in industrial and commercial scenarios, engineers and developers are often faced with the requirement of constrained time budget. In this paper, we investigate the accuracy of CNNs under constrained time cost. Under this constraint, the designs of the network architectures should exhibit as trade-offs among the factors like depth, numbers of filters, filter sizes, etc. With a series of controlled comparisons, we progressively modify a baseline model while preserving its time complexity. This is also helpful for understanding the importance of the factors in network designs. We present an architecture that achieves very competitive accuracy in the ImageNet dataset (11.8% top-5 error, 10-view test), yet is 20% faster than "AlexNet" (16.0% top-5 error, 10-view test).