Computation offloading has effectively solved the problem of terminal devices computing resources limitation in hospitals by shifting the medical image diagnosis task to the edge servers for execution. Appropriate offloading strategies for diagnostic tasks are essential. However, the risk awareness of each user and the multiple expenses associated with processing tasks have been ignored in prior works. In this article, a multi-user multi-objective computation offloading for medical image diagnosis is proposed. First, the prospect theoretic utility function of each user is designed considering the delay, energy consumption, payment, and risk awareness. Second, the computation offloading problem including the above factors is defined as a distributed optimization problem, which with the goal of maximizing the utility of each user. The distributed optimization problem is then transformed into a non-cooperative game among the users. The exact potential game proves that the non-cooperative game has Nash equilibrium points. A low-complexity computation offloading algorithm based on best response dynamics finally is proposed. Detailed numerical experiments demonstrate the impact of different parameters and convergence in the algorithm on the utility function. The result shows that, compare with four benchmarks and four heuristic algorithms, the proposed algorithm in this article ensures a faster convergence speed and achieves only a 1.14% decrease in the utility value as the number of users increases.