MIMA-MAC is the most attractive MAC protocol for MIMO ad hoc networks, which consist of nodes with multiple antennas. MIMA-MAC, however, uses only a half of antennas for data transmission regardless of the number of antennas or transmission demands of neighboring nodes. In this paper, we propose a MAC protocol for MIMO ad hoc networks with Parallel RTS Processing (PRP-MAC) which determines the maximum allowable number of data streams after receiving up to 2 RTS packets at a receiver. PRP-MAC can maximize the number of transmitted data streams regardless of collision of RTS packets, the number of transmission demands from neighboring nodes and the number of antennas at each node. Our simulation results show that PRP-MAC can enhance the network throughput, and decrease the amount of control bytes per data packet compared with MIMA-MAC. In addition, we also show the availability of PRP-MAC in antenna-heterogeneous environments.