Continual learning (CL), the problem of lifelong learning where tasks arrive in sequence, has attracted increasing attention in the computer vision community lately. The goal of CL is to learn new tasks while maintaining the performance on the previously learned tasks. There are two major obstacles for CL of deep neural networks: catastrophic forgetting and limited model capacity. Inspired by the recent breakthroughs in automatically learning good neural network architectures, we develop a nonexpansive AutoML framework for CL termed Regularize, Expand and Compress (REC) to solve the above issues. REC is a unified framework with three highlights: 1) a novel regularized weight consolidation (RWC) algorithm to avoid forgetting, where accessing the data seen in the previously learned tasks is not required; 2) an automatic neural architecture search (AutoML) engine to expand the network to increase model capability; 3) smart compression of the expanded model after a new task is learned to improve the model efficiency. The experimental results on four different image recognition datasets demonstrate the superior performance of the proposed REC over other CL algorithms.