Recent studies on neural architecture search have shown that automatically designed neural networks perform as good as expert-crafted architectures. While most existing works aim at finding architectures that optimize the prediction accuracy, these architectures may have complexity and is therefore not suitable being deployed on certain computing environment (e.g., with limited power budgets). We propose MONAS, a framework for Multi-Objective Neural Architectural Search that employs reward functions considering both prediction accuracy and other important objectives (e.g., power consumption) when searching for neural network architectures. Experimental results showed that, compared to the state-ofthe-arts, models found by MONAS achieve comparable or better classification accuracy on computer vision applications, while satisfying the additional objectives such as peak power.