3D hand pose estimation is an important task for a wide range of real-world applications. Existing works in this domain mainly focus on designing advanced algorithms to achieve high pose estimation accuracy. However, besides accuracy, the computation efficiency that affects the computation speed and power consumption is also crucial for real-world applications. In this paper, we investigate the problem of reducing the overall computation cost yet maintaining the high accuracy for 3D hand pose estimation from video sequences. A novel model, called Adaptive Computationally Efficient (ACE) network, is proposed, which takes advantage of a Gaussian kernel based Gate Module to dynamically switch the computation between a light model and a heavy network for feature extraction. Our model employs the light model to compute efficient features for most of the frames and invokes the heavy model only when necessary. Combined with the temporal context, the proposed model accurately estimates the 3D hand pose. We evaluate our model on two publicly available datasets, and achieve state-of-the-art performance at 22% of the computation cost compared to traditional temporal models.