In this paper, we suggest criteria for objective measurement of speech quality in mobile VoIP (Voice over Internet Protocol) services over wireless mobile internet such as mobile WiMAX networks. This is the case that voice communication service is available under other networks. When mobile VoIP service users in the mobile internet network based on packet call up PSTN and mobile network users, but there have not been relevant quality indexes and quality standards for evaluating speech quality of mobile VoIP. In addition, there are many factors influencing on the speech quality in packet network. Especially, if the degraded speech with packet loss transfers to the other network users through the handover, voice communication quality is significantly deteriorated by the transformation of speech codecs. In this paper, we eventually adopt the Gilbert-Elliot channel model to characterize packet network and assess the voice quality through the objective speech quality method of ITU-T P. 862. 1 MOS-LQO for the various call scenario from mobile VoIP service user to PSTN and mobile network users under various packet loss rates in the transmission channel environments. Our simulation results show that transformation of speech codecs results in the degraded speech quality for different transmission channel environments when mobile VoIP service users call up PSTN and mobile network users.