In this technical note, a new class of discrete-time networked nonlinear systems with mixed random delays and packet dropouts is introduced, and the H-infinity filtering problem for such systems is investigated. The mixed stochasitc time-delays consist of both discrete and infinite distributed delays and the packet dropout phenomenon occurs in a random way. Furthermore, new techniques are presented to deal with the infinite distributed delay in the discrete-time domain. Sufficient conditions for the existence of an admissible filter are established, which ensure the asymptotical stability as well as a prescribed H-infinity performance. Finally, examples are given to demonstrate the effectiveness of the proposed filter design scheme in this technical note.