Herein, a method for generating tunable nonparaxial accelerating beams is proposed theoretically by spectral phase modulation and verified experimentally. The mathematical model of the relationship between spectral phase and beam propagation trajectory is established based on the stationary phase approximation and the principle of optical caustics. Theoretical simulations and experimental results show that the proposed method overcomes the limitations of conventional paraxial approximation, and nonparaxial accelerating beams are generated. Such accelerating beams with flexible and tunable trajectories have potential applications in the areas of optical particle manipulation, particle transport and guidance, and super-resolution imaging.