Driven by the demand for high-speed transmission in short-reach multimode fiber optic communication, the coupling scheme of single-mode optical modules with existing multimode fibers holds significant engineering value. A mode excitation model for single-mode to multimode fiber (SMF-MMF) coupling is established, and analytical expressions for the coupling coefficient and bit error rate (BER) are derived. For Grade A, B, and C fiber connectors, the effects of axial gap, lateral offset, and angular misalignment on mode excitation and BER are systematically investigated. The results show that: the axial gap has a negligible impact on mode excitation; under ideal alignment, the light from the single-mode fiber only excites the LP0p modes in the multimode fiber; both lateral offset and angular misalignment cause power coupling from the LP0p mode to other modes, with the lateral offset exerting a more prominent effect. The BERs under the ideal condition and the extreme connection conditions of the three connector grades are calculated. The results indicate that the BER of Grade C connectors deteriorates by nearly two orders of magnitude compared to the ideal case, and the logarithm of the BER shows a positive linear correlation with the product of the transmission rate and distance. This research provides theoretical reference for the design of SMF-MMF transmission systems and offers engineering optimization guidelines for the low-cost upgrade of short-reach optical networks.