The invention discloses an AZ61 magnesium alloy with weak-basal/non-basal texture and low anisotropy, and a preparation method of the AZ61 magnesium alloy, and belongs to the technical field of magnesium alloy plastic processing. A molten AZ61 magnesium alloy is subjected to solid-solution treatment at a deformation temperature of 250-350 DEG C. Continuous cyclic hammer forging is performed through an industrial air hammer forging machine along three axial directions orthogonal to one another; one time of hammer forging in one direction is one pass; and the direction is changed every pass of hammer forging. Strain of each pass is 3-10%, and an average strain rate of hammer forging is 15-200 s<-1>. Hammer forging is continuously performed for 20-250 passes. The grain size of a hammer-forged sample is 12-30 [mu]m; the texture peak intensity is less than 6; a deviation angle of a texture peak location relative to a pole figure center is more than 30 degrees. In each direction of the sample, yield strength sigma, tensile strength sigma, and elongation percentage sigma are no less than 90 MPa, 270 MPa, and 20%, respectively.