Currently, Underwater Wireless Sensor Network (UWSN) is one of modern science and have attached many researchers especially how interesting with Wireless Sensor Network (WSN). A mobile node in UWSN is one of the powerful mechanisms, it can be used for many aquatic applications such as Surveillance for wildlife, Pollution control, Military applications, etc. UWSN is different from the terrestrial network in terms of using acoustic waves as a communication medium. Due limitation of bandwidth, high latency, and long propagation delay of acoustic waves, many proper MAC protocols that work efficiently in Static UWSN are not suitable for the mobile network. In this article two MAC protocols appropriate for mobile underwater network Broadcast as Direct access and geo-routing aware MAC protocol (GOAL) as Handshaking are evaluated, in both static and mobile nodes with respect to throughput, energy consumption, and delay. Then the effect of using Multi-Sink on the performance is shown, the evaluation is done based on AquaSim simulator, Aqua3D Animator, and AWK programming language have been used to extract the results. As a result, the performance has been improved by using multi-Sink with two types of MAC address, and for all the metrics.