In this paper, we investigate block-coded QAM constructed by multilevel coding for the noncoherent generalized likelihood ratio test (GLRT) detector. For the AWGN channel, we derive a new GLRT detector and the corresponding distance. The minimum noncoherent distance of block-coded QAM is derived and two construction of noncoherent block-coded QAM (NBC-QAM) are proposed accordingly. In the NBC-QAM scheme, the error performance can be optimized by adjusting the constellation. The superior error performances of NBC-QAM are verified by simulation results.