The invention discloses a unipolar ringless wide hysteresis control device and method for grid-connected current of a single-phase grid-connected inverter, which belongs to the field of conversion of electrical energy, and is used for solving the problem that the subversion and maximum switching frequency of the grid-connected current are uncontrollable in the existing control methods. The method provided by the invention comprises the following steps: 1, adding a DC (direct current) offset to an acquired instantaneous value i of an grid-connected current so as to obtain offset instantaneous values i t, which greater than zero in the whole electric cycle, of the grid-connected current; acquiring an instantaneous values e of a grid voltage, and generating a square signal synchronous with the grid voltage; and setting the amplitude value Im* of a given grid-connected current; 2, obtaining an instantaneous value I* of the given grid-connected current; 3, when the cycle of a timer arrives, generating two paths of switch signals as the control signals of a second bridge arm according to the i* and the i t; and 4, generating two paths of switch signals as the control signals of a first bridge arm according to the square signal synchronous with the grid voltage, thereby realizing the unipolar ringless wide hysteresis control for the grid-connected current of the single-phase grid-connected inverter.