This paper presents a novel level set-based topology optimization method that incorporates the augmented Lagrangian method. In previously proposed level set-based topology optimization methods, dealing with multiple constraints has been problematic; nonetheless, this remains a typical requirement of real-world design problems. Herein, the augmented Lagrangian method is incorporated in a level set-based topology optimization method to enable the handling of multiple constrains. The level set function is discretized using finite elements and updated based on the design sensitivity of the augmented Lagrangian with respect to the discretized level set function. In this paper, the newly proposed method is applied to the minimum compliance problem and a compliant mechanism design problem. In the formulations of these problems, a perimeter constraint is imposed to overcome the ill-posedness of level set-based topology optimization. Some numerical examples that include multiple constraints are provided to confirm the validity of the proposed method, and we show that appropriate optimal structures are obtained.