In-phase and quadrature-phase (I/Q) imbalance is a critical issue limit the achievable operating signal-to-noise ratio (SNR) at the receiver in direct conversion architecture. In recent literatures, the second-and fourth-order circularity property of communication signals have been used for designing compensator to eliminate the I/Q imbalance. In this paper, we investigate whether moment circularity of an order higher than four can be used in receiver I/Q imbalance compensation. It is shown that the sixth-order moment E[z4z*2] is a suitable statistic for measuring the sixth-order circularity of representative communication signals such as M-QAM and M-PSK with M > 2. Two blind algorithms are then proposed to update the coefficients of I/Q imbalance compensator by restoring the sixth-order circularity of the compensator output signal. Simulation results show that the new proposed methods based on sixth-order statistic converges faster or gives lower steady-state variance than the reference methods that are based on second-and fourth-order statistics.