Heavy duty pneumatic tires having lug grooves at a tire tread surface are disclosed, wherein a width of a tread portion from a tire equator to one of tread edges which tread portion is to be located on a wheel-mounted outer side is larger than that of the other tread portion from the equator to the other tread edge. When contours of the tread portions located on the opposite sides of the tire equator are approximated by two respective circular arcs, the radius of curvature of the wider tread portion is larger than that of the narrower tread portion. A depth of grooves at the shoulder portion on the wider tread portion which depth is expressed by a distance between the tread edge and the bottom of the lug grooves is made smaller than that of the narrower tread portion.