The present invention provides a process of preparing terephthalic acid of high quality which is characterized by:oxidizing p-xylene with molecular oxygen in an acetic acid solvent in the presence of a catalyst comprised of at least one heavy metal and bromine at a temperature of from 180.degree. to 230.degree. C. to convert at least 95 wt % of the p-xylene into terephthalic acid and, optionally, subjecting the resultant reaction mixture to low temperature post-oxidation with molecular oxygen at temperatures lower than the temperature of the first oxidation reaction, thereby obtaining a slurry containing terephthalic acid particles whose spectral reflectance defined below is not less than 70% and whose reflectance ratio (400/500) defined below is not less than 0.92;subjecting the slurry to high temperature post-oxidation with molecular oxygen at a temperature of from 235.degree. to 290.degree. C. and then to crystallization; andcollecting the resultant terephthalic acid from the reaction mixture.Spectral reflectance=a spectral reflectance at 500 nm determined according to a white light illumination method.Reflectance ratio (400/500)=(spectral reflectance at 400 nm)/(spectral reflectance at 500 nm).