Mobile edge computing (MEC) enables the caching of various services close to users, thereby reducing service delay for emerging applications. However, realizing efficient and secure computation offloading is challenging due to the limited storage capacity of MEC servers and the offloading security issue arising from the open nature of wireless channels. In this letter, we investigate a MEC network with an eavesdropper, where the MEC server caches service programs required for task execution. Moreover, we propose a cooperative jamming-assisted scheme to enhance the security of computation offloading, in which a friendly jammer actively transmits signals to disrupt eavesdropping. Considering the limited caching capacity of the MEC server and the security concerns of computation offloading, we formulate a delay minimization problem by jointly optimizing service caching placement, transmit power, and devices' computation offloading decisions. To tackle this problem, we develop an efficient layered algorithm using successive convex approximation and the cross entropy-based technique. Numerical results demonstrate the effectiveness of our proposed scheme in reducing the overall delay in completing devices' computation tasks compared to baseline schemes.