AbstractIn this paper, Hirota’s bilinear method is extended to a new modified Kortweg–de Vries (mKdV) hierarchy with time-dependent coefficients. To begin with, we give a bilinear form of the mKdV hierarchy. Based on the bilinear form, we then obtain one-soliton, two-soliton and three-soliton solutions of the mKdV hierarchy. Finally, a uniform formula for the explicitN-soliton solution of the mKdV hierarchy is summarized. It is graphically shown that the obtained soliton solutions with time-dependent functions possess time-varying velocities in the process of propagation.