Accurate measurement of beam quality in laser communication optical transceivers is crucial for their design, assembly, and application. This paper presents a large-aperture off-axis beam quality measurement system that utilizes complex amplitude reconstruction. The proposed system captures intensity and relative position information by focusing on an off-axis parabolic surface. The transport of intensity equation (TIE) is then employed to reconstruct the complex amplitude of the focused beam. Angular spectrum theory is applied to determine the beam's intensity distribution in space, thereby enabling rapid measurement of the beam quality factor M2. The proposed large-aperture off-axis focusing system effectively overcomes the aperture limitations of typical optical transceiver output beams. Optical simulations are used to analyze the system accuracy requirements to ensure precise measurements. The phase reconstruction process, achieved through purely numerical analysis using the TIE, is unaffected by amplitude variations in the focused beam field. Compared to ISO international standards, the proposed system achieves measurement accuracy with errors controlled within 4%. The experimental setup avoids the need for complex optical equipment, thus reducing the time required for multiple sampling steps. In addition, the proposed system provides a fast and accurate method for measuring laser communication optical transceivers, offering a technical means for dynamic quality detection.