The key problem for simulating mass transfer in multi solvent systems is the concentration jump at the phase interface described by Henry's law. In the present paper, after analyzing the shortages of Fick's law in describing mass transfer in multi solvent systems, the revised Fick's law that can be applied to mass transfer in multi solvent systems is proposed. The corresponding governing equation can describe the concentration jump directly without any modification and doesn't need to transform the scalar or parameters. To solve the governing differential equation based on the revised Fick's law, a multi-relaxation-time (MRT) lattice Boltzmann equation (LBE) is constructed. Five test cases containing both the transient and steady mass transfer problems in multi solvent systems with straight or curved interfaces are conducted to validate the proposed MRT LBE. The results show that proposed MRT LBE is easy in implementation and capable of simulating both steady and transient mass transfer in multi solvent systems. In addition, the comparison indicates that the MRT LBE could have better accuracy than single-relaxation-time (SRT) LBE by keeping an optimal relation between two relaxation times. (C) 2018 Elsevier Ltd. All rights reserved.