In this paper, we propose a new digital blind in-phase/quadrature-phase (I/Q) mismatch compensation technique for image rejection in a direct-conversion receiver (DCR). The proposed image-rejection circuit adopts DC offset cancellation and a sign-sign least mean squares (LMS) algorithm with a unique step size adaptation both for a fast and precise I/Q mismatch estimation. In addition, several performance-optimizing design considerations related to accuracy, speed, and hardware simplicity are discussed. The implementation of the proposed circuit in an FPGA results in an image-rejection ratio (IRR) of 65 dB, which is the best performance with modulated signals, along with an adaptation time of 0.9 seconds, which is a tenfold increase in the compensation speed as compared to previously reported circuits. The proposed technique will be a promising solution in the area of image rejection to increase both the speed and accuracy of future DCRs.