It is well known that the MaxWeight scheduling algorithm is throughput-optimal in wireless networks. However, its complexity is exponential in the number of links in an ad hoc wireless network. In this work, we consider a greedy variant of the MaxWeight algorithm, called Longest Queue First (LQF) algorithm. A synchronous version of LQF algorithm is known to be throughput-optimal under a topological condition called local pooling. Here we study an asynchronous version which is suitable for implementation in networks with variable packet sizes. We show that the asynchronous LQF algorithm is also throughput-optimal under the local pooling condition.