We aim to obtain high-quality time-resolved spectral fits of gamma-ray bursts observed by the Gamma-ray Burst Monitor (GBM) on board the Fermi Gamma-ray Space Telescope. We performed time-resolved spectral analysis with high temporal and spectral resolution of the brightest bursts observed by Fermi GBM in its first four years of mission. We present the complete catalog containing 1491 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 three bursts (36 spectra in total) show evidence of a pure Planck function. It is observed that peak energy and the averaged, time-resolved power-law index at low energy are slightly harder than the time-integrated values. Time-resolved spectroscopic results should be used instead of time-integrated results when interpreting physics from the observed spectra.