The object of the present invention is to provide an Ni-based single crystal super alloy capable of improving strength by preventing precipitation of a TCP phase at high temperatures. This object is achieved by an Ni-based single crystal super alloy having a composition comprising 5.0-7.0 wt % of Al, 4.0-10.0 wt % of Ta, 1.1-4.5 wt % of Mo, 4.0-10.0 wt % of W, 3.1-8.0 wt % of Re, 0-0.50 wt % of Hf, 2.0-5.0 wt % of Cr, 0-9.9 wt % of Co and 4.1-14.0 wt % of Ru in terms of its weight ratio, with the remainder consisting of Ni and unavoidable impurities. Furthermore, in this Ni-based single crystal super alloy, when lattice constant of matrix is taken to be a1 and lattice constant of precipitation phase is taken to be a2, a2≦0.999a1.