This paper investigates low‐latency offloading strategy in a non‐orthogonal multiple access aided mobile edge computing (NOMA‐MEC) system consisting of K edge servers, one mobile user and one cloud server. An intelligent edge server selection strategy (IESSS) based on Markov decision process (MDP) is proposed to select an edge server, in order to reduce the task completion latency of this system. When an edge server is selected by the proposed IESSS, a joint optimization problem of power allocation and task scheduling factors is formulated to minimize the task completion latency of the hybrid NOMA‐MEC system. To solve the formulated non‐convex optimization problem with coupled variables, a low‐complexity adaptive power‐task resource allocation iterative (APTRAI) algorithm is proposed. Simulation results demonstrate the advantages of the proposed IESSS and verify the convergence and time complexity of the proposed APTRAI algorithm.