This paper investigates secure computation offloading for an intelligent reflecting surface (IRS)-assisted mobile edge computing (MEC) network. Specifically, wireless devices offload partial computation tasks to an access point integrated with a MEC server. During this process, an eavesdropper tries to overhear the private information of devices. We propose an IRS-assisted secure offloading scheme that adjusts the phase of the IRS to improve the security of computation offloading. We aim to maximize the minimum secrecy rate of devices by jointly optimizing the transmit power of devices for computation offloading, the computation task partitions, and the passive beamforming of the IRS while satisfying the offloading rate constraint and the energy budget constraint. To deal with the formulated highly non-convex problem, we develop a block coordinate descent-based algorithm that decouples the problem into two subproblems of optimizing resource allocation and passive beamforming. Besides, successive convex approximation and semidefinite relaxation are exploited to solve the two subproblems. Simulation results demonstrate that our designed scheme yields a performance enhancement compared to benchmarks.