With the explosive proliferation of mobile devices, mobile crowdsourcing has become a new paradigm involving a crowd of mobile users to collectively take large-scale tasks required by requesters in mobile social networks (MSNs). In this paper, we work on new task allocation schemes for mobile crowdsourcing in Opportunistic Mobile Social Networks (OMSNs) which are formed opportunistically when people gather together. Our goal is to distribute the tasks to the minimum number of users using the minimum number of forwarders quickly. Our task allocation problem is related to the set cover problem which is NP-hard. To solve it, we put forward a heuristic opportunistic task allocation approximation (OTAA) algorithm where we use a consumer control criterion to reduce the number of consumers and a forwarder control criterion to select the best forwarder. After the analysis of two typical OMSN traces, we find it better to delegate all the tasks to the selected forwarder to reduce latency. Simulation results comparing our proposed algorithm with its variations using the two OMSN traces confirm that our proposed algorithm exhibits a high success rate, lowest latency, and uses small numbers of consumers and forwarders.