In this paper, we discuss a computation offloading in mobile edge computing (MEC) systems. We especially focus on the case where a mobile node sends calculation requests to surrounding access points (APs) that have the computational capability. Unlike wired distributed computing systems, MEC systems suffer from the unstable connectivity due to wireless channel fluctuations such as multipath fading and shadowing effect; there is a possibility that the calculation results disappear by loss of wireless connectivity. In order to maximize the offloading effect in the wireless environment, we propose radio environment aware task allocation methods with predicting wireless connectivity between the mobile node and APs. Especially, we discuss two methods: radio environment map (REM)-based connectivity prediction and distance-based one. Numerical results show that the proposed method can effectively offload the computation tasks compared with conventional methods that ignore the wireless connectivity.