Abstract: Objectives Stiffness optimization of elastic supports is one of the common methods to achieve the optimal assignment of the natural frequencies of fluid-conveying pipeline and to solve the problem of pipeline resonance. The optimal stiffness calculated using optimization algorithms is mostly a kind of continuous-optimal parameter. In practice, those continuous-optimal stiffness parameter is often discretized by the closest principle, which may make the optimal assignment of natural frequency deviate from the target value, resulting in unsatisfactory vibration reduction. Methods In order to solve this problem, this paper proposes a novel method for optimizing the natural frequency of fluid-conveying pipelines based on the discrete stiffness of elastic supports. Such a method uses the sensitivity formula of the target natural frequency to stiffness parameters derived in this paper as the core algorithm and takes the continuous-optimal stiffness parameters as the initial value. The discrete-optimal stiffness parameters of elastic supports are solved by minimizing the disturbance deviation between the natural frequency and the target frequency. Results The proposed method was demonstrated by employing both numerical and experimental models of a U-shaped fluid-conveying pipeline. The results show that the discrete-optimal stiffness parameters obtained by using the proposed method can accurately achieve optimization assignment of the first three natural frequencies of the U-shaped fluid-conveying pipeline. Conclusions The method proposed in this paper has a fast computation speed, good convergence, and can significantly reduce the disturbance deviation of the assigned natural frequencies. The proposed method can effectively address the issue of suboptimal natural frequency optimization results caused by errors between the continuously optimal stiffness from calculations and the discrete stiffness in implementation, which provides technical support for the engineering application of stiffness optimization methods.