Motivated by a problem concerning multi-valued mappings posed by Reich [S. Reich, Some fixed point problems, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 57 (1974) 194–198] and a paper of Jleli and Samet [M. Jleli, B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl. 2014:38 (2014) 1–8], we consider a new class of multi-valued mappings that satisfy a Φ-contractive condition in complete metric spaces and prove some fixed point theorems. These results generalize Reich's and Mizoguchi-Takahashi's fixed point theorems. Some examples are given to show the usability of the obtained results.