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Dark energy is believed to be responsible for the acceleration of the Universe. In this paper, we reconstruct the dark energy scalar field potential V ( ϕ ) using the Hubble parameter H ( z ) through Gaussian process analysis. Our goal is to investigate dark energy using various H ( z ) data sets and priors. We find that the selection of the prior and the H ( z ) data set significantly affects the reconstructed V ( ϕ ). We compare two models, Power Law and Free Field, to the reconstructed V ( ϕ ) by computing the reduced chi-square. The results suggest that the models are generally in agreement with the reconstructed potential within a 3 σ confidence interval, except in the case of Observational H ( z ) data with the Planck 18 prior. Additionally, we simulate H ( z ) data to measure the effect of increasing the number of data points on the accuracy of reconstructed V ( ϕ ). We find that doubling the number of H ( z ) data points can improve the accuracy rate of reconstructed V ( ϕ ) by 5%–30%.