Based on the fourth moment technique, the reliability0-based optimization design theory, the reliability sensitivity technique and the robust design method, the reliability-based robust design of coil tube spring with non-normal random parameters is extensively discussed and a numerical method for reliability  based robust design is proposed. The reliability sensitivity is added to the reliability-based optimization design model and the reliability-based robust design is described as a multi-objection optimization. On the condition of known first four moments of basic random variables, the respective program can be used to obtain the reliability-based robust design information of coil tube-spring with non-normal random parameters accurately and quickly. According to the numerical results, the approach proposed is a convenient and practical reliability-based roust design method.