Hyperons constitute an important sector in hadron physics, their large number provides a valuable platform for studying their properties and plays a significant role in hadron spectroscopy. Based on the extensive experimental observations of hyperons, this work employs the Capstick–Isgur model to calculate the spectra of Λ, Σ, and Ξ hyperons by solving the three-body Schrödinger equation. We obtain the parameters of the potential model with spectra of the well established baryons, and calculate the masses of S-, P-, and D-wave Λ, Σ, and Ξ baryons. We present numerical results of 1S, 2S, 1P, and several lower D-wave states. The calculated spectra are compared with existing experimental results. For the Λ and Σ, the theoretical masses match the experimental results pretty well with 1S. For the 1P, 2S, and the lower D-wave states, there exists some good candidates. For the Ξ, the masses of 1S states are consistent with the experimental results well. And there are also good \Xi(1P) candidates, which match our calculations. On one hand, this allows us to analyze the properties of known hyperons and explore their possible positions within the hyperon family, on the other hand, it enables us to predict additional, yet-to-be-discovered hyperons, offering theoretical guidance for future experiments. Besides the numerical results presented, there are also many observed states which masses are much higher than our calculations, leaving considerable scope for further investigation. In addition to the mass spectra, we also analyze the impact of parameter variations on the masses, which help us to understand the contributions of each parameter in the spectra. This study aims to provide theoretical support for hyperon spectroscopy experiments planned by Collaborations such as BESIII, LHCb, Belle II, and so on. We look forward to the discovery of more hyperons in upcoming experiments, which will contribute to refining the field of hyperon spectroscopy.