For quick segmentation and denoising, the classical Mumford-Shah (MS) model needs to enhance the penalization term,i.e. to increase the penalization parameter, which leads to gradual disappearance of objects. In this paper, we propose an improved Mumford-Shah (IMS) model to avoid the phenomenon, and adopt the piecewise constant level set method (PCLSM) and the gradient descent method to solve the minimization problem. Numerical experiments are given to show the efficiency and advantages of the new model and the algorithms.