In status update scenarios, the freshness of information is measured in terms of age-of-information (AoI), which essentially reflects the timeliness for real-time applications to transmit status update messages to a remote controller. For some applications, computational expensive and time consuming data processing is inevitable for status information of messages to be displayed. Mobile edge servers are equipped with adequate computation resources and they are placed close to users. Thus, mobile edge computing (MEC) can be a promising technology to reduce AoI for computation-intensive messages. In this paper, we study the AoI for computation-intensive messages with MEC, and consider three computing schemes: local computing, remote computing at the MEC server, and partial computing, i.e., some part of computing tasks are performed locally, and the rest is executed at the MEC server. Zero-wait policy is adopted in all three schemes. Specifically, in local computing, a new message is generated immediately after the previous one is revealed by computing. While in remote computing and partial computing, a new message is generated once the previous one is received by the remote MEC server. With infinite queue size and exponentially distributed transmission time, closed-form average AoI for exponentially distributed computing time is derived for the three computing schemes. For deterministic computing time, the average AoI is analyzed numerically. Simulation results show that by carefully partitioning the computing tasks, the average AoI in partial computing is the smallest compared to local computing and remote computing. The results also indicate numerically the conditions on which remote computing attains smaller average AoI compared with local computing.