We aim to obtain high-quality time-resolved spectral fits of gamma-ray bursts (GRBs) observed by the Gamma-ray Burst Monitor (GBM) on board the Fermi Gamma-ray Space Telescope. We perform time-resolved spectral analysis with high temporal and spectral resolution of the brightest bursts observed by Fermi GBM in its first 4 years of mission. We present the complete catalog containing 1,491 spectra from 81 bursts with high spectral and temporal resolution. Distributions of parameters, statistics of the parameter populations, parameter-parameter and parameter-uncertainty correlations, and their exact values are obtained and presented as main results in this catalog. We report a criterion that is robust enough to automatically distinguish between different spectral evolutionary trends between bursts. We also search for plausible blackbody emission components and find that only 3 bursts (36 spectra in total) show evidence of a pure Planck function. It is observed that the averaged time-resolved low-energy power-law index and peak energy are slightly harder than the time-integrated values. Time-resolved spectroscopic results should be used when interpreting physics from the observed spectra, instead of the time-integrated results.