This study presents the black hole accretion history (BHAH) of obscured active galactic nuclei (AGNs) identified from the JWST CEERS survey by Chien et al. (2024) using mid-infrared (MIR) SED fitting. We compute black hole accretion rates (BHARs) to estimate the black hole accretion density (BHAD), ρLdisk, across 0 < z < 4.25. MIR luminosity functions (LFs) are also constructed for these sources, modeled with modified Schechter and double power law forms, and corresponding BHAD, ρLF, is derived by integrating the LFs and multiplying by the luminosity. Both ρLF extend to luminosities as lowas 107 L⊙, two orders of magnitude fainter than pre-JWST studies. Our results show that BHAD peaks between redshifts 1 and 3, with the peak varying by method and model, z ≃ 1 - 2 for ρLdisk and the double power law, and z ≃ 2 - 3 for the modified Schechter function. A scenario where AGN activity peaks before cosmic star formation would challenge existing black hole formation theories, but our present study, based on early JWST observations, provides an initial exploration of this possibility. At z ∼ 3, ρLF appears higher than X-ray estimates, suggesting that MIR observations are more effective in detecting obscured AGNs missed by X-ray observations. However, given the overlapping error bars, this difference remains within the uncertainties and requires confirmation with larger samples. These findings highlight the potential of JWST surveys to enhance the understanding of co-evolution between galaxies and AGNs.