From the point of view of insufficient statistical data, a non-probabilistic reliability method for implicit performance function of geotechnical engineering is developed, which is a useful complement to the probabilistic reliability method. Firstly, we use the series of interval extension functions to reduce the interval correlation, and establish the iterative program for implicit function interval solution based on the subinterval method. Then, the experiment design is utilized to establish the statistical optimization model from the point view of comprehensive design to search the optimal solution and further to achieve a target range. Finally, by setting the confidence interval for the interval solution to stress function in the performance function, the non-probabilistic reliability model of the implicit performance function with limited computational cost is obtained. Moreover, through the solution for external function of support pressure, the detailed operation procedures of the non-probabilistic method are demonstrated. The results of the engineering examples show that the relative error between the maximum support resistance obtained by the proposed method and the maximum value of Monte-Carlo simulation is 0.83%, and the proposed method has a preference for absolute security.