In this article, by introducing a new operator, we give a new generalized contraction condition for multivalued maps. Moreover, without assumption of lower semi-continuity, we prove some fixed point theorems in incomplete metric spaces. Our results are extension of the corresponding results of I. Altun et al. (Nonlinear Analysis: Modeling and control, 2016, Vol. 21, No. 2, 201--210). Also, we provide some examples to show that our main theorem is a generalization of some previous results.