Various structural optimization methods have been proposed for design problems in many industries, such as mechanical, automotive, aerospace and civil industries. Recently, some structural optimization methods based on the level set method have been proposed. Although the previously proposed level set method-based structural optimization methods have some benefits, these methods have a difficulty with respect to updating the level set function. Therefore we proposed a new structural optimization method based on the level set method where the level set function is updated based on a simple scheme. In this paper, the newly proposed method is applied to vibration problems and heat conduction problems, and several numerical examples are provided to demonstrate that appropriate optimal structures can be obtained using the newly proposed method.