We propose a superconducting circuit based on the Bloch transistor, a quantum device consisting of two small-capacitance Josephson junctions connected in series and having a small island in between. This device is driven by two dc electrical sources controlling Josephson oscillations of frequency f_J = 2eV_J̄/h, related to the average voltage V_J̄ on the transistor, and Bloch oscillations of frequency f_B = I_B̄/2e, related to the average current I_B̄ injected into the transistor island. Due to the Bloch transistor properties, these two types of oscillations can mutually phase lock, i.e., f_J = f_B. This leads to formation of current steps on the current-voltage curve at Ī_B = 2ef_J, which are similar to the dual Shapiro steps appearing at current Ī=2ef under microwave irradiation of frequency f. Moreover, transconductance I_B̄/V_J̄ takes the fundamental value of 1/R_Q, where R_Q = h/4e² is the resistance quantum. The obtained results pave the way to the alternative quantum standard of resistance, based on the superconducting circuit and operating without applying strong magnetic field.