A color converting apparatus is provided with a table memory for storing pieces of color converting data defined in an output color space at color converting addresses, and a signal receiving section for receiving three signals designating an input color in a lightness-color difference space. The color converting addresses are placed at lattice points of cubic blocks formed by partitioning the lightness-color difference space in a lightness direction and first and second color difference directions. Each of the cubic blocks has the lattice points Pa, Pb, Pc and Pd at its lower plane and the lattice points Pe, Pf, Pg and Ph at its upper plane. Each of the cubic blocks is partitioned into a first triangular prism having the lattice points Pa, Pb, Pc, Pe, Pf and Pg and a second triangular prism having the lattice points Pa, Pd, Pc, Pe, Ph and Pg. A particular triangular prism in which the input color is included is specified, and six pieces of color converting data Da, Db (or Dd), Dc, De, Df (or Dh) and Dg addressed at the lattice points Pa, Pb (or Pd), Pc, Pe (or Ph), Pf of the particular triangular prism are read out from the table memory, and an output color which corresponds to the input color and is defined in the output space is interpolated with the color converting data read out.