We describe the equations of the Rees algebra R(I) of an equimultiple ideal I of deviation one provided that I has a reduction generated by a regular sequence x1, . . . , xs such that the initial forms x∗ 1, . . . , x∗ s−1 are a regular sequence in the associated graded ring. In particular, we prove that there is a single equation of maximum degree in a minimal generating set of the equations of R(I), which recovers some previous known results.