This paper focuses on studying the performance of TPGF geographic routing algorithm with multi routing metric called McTPGF in random duty-cycled wireless multimedia sensor networks (WMSNs). The multi-metric contains the geographic distance and the time, which is called sleeping-delay in this paper, the forwarding node waits to forward packet to the neighbor node after it wakes up. We recognize the fact that in random duty-cycled WMSNs, geographic routing should not only consider the geographic distance of the neighbor node but also the sleeping-delay of the node at that moment. The significant difference between our work and the TPGF is that our work pays more attentions to the demand of finding a single routing path with low sleeping-delay at a certain time using TPGF while the traditional TPGF algorithm focuses on finding all node-disjoint paths in the given network topology. Simulations are conducted to evaluate that the McTPGF reduces the end-to-end delay with the cost of adding few hop counts compared with the traditional TPGF algorithm in random duty-cycled WMSNs.