This paper presents a linear equating procedure which is applicable to the incomplete data of an essay-type test scored by several raters. The procedure is based on a two-step optimizing criterion. In the first step, weight parameters are estimated in order to mutually equate dispersions of raters. In the second step, additive constants for equating means are obtained on condition that weight parameters are fixed. A numerical example is given to illustrate the efficacy of the procedure.