We present results of three dimensional numerical simulations of the merger of unequal-mass binary neutron stars in full general relativity. A Gamma-law equation of state P=(Gamma-1)rhoepsilon is adopted, where P, rho, epsilon, and Gamma are the pressure, rest mass density, specific internal energy, and the adiabatic constant, respectively. We take Gamma=2 and the baryon rest-mass ratio Q(M) to be in the range 0.85-1. The typical grid size is (633,633,317) for (x,y,z). We improve several implementations since the latest work. In the present code, the radiation reaction of gravitational waves is taken into account with a good accuracy. This fact enables us to follow the coalescence all the way from the late inspiral phase through the merger phase for which the transition is triggered by the radiation reaction. It is found that if the total rest mass of the system is more than similar to1.7 times of the maximum allowed rest mass of spherical neutron stars, a black hole is formed after the merger, irrespective of the mass ratios. The gravitational waveforms and outcomes in the merger of unequal-mass binaries are compared with those in equal-mass binaries. It is found that the disk mass around the so formed black holes increases with decreasing rest-mass ratios and decreases with increasing compactness of neutron stars. The merger process and the gravitational waveforms also depend strongly on the rest-mass ratios even for the range Q(M)=0.85-1.