The dynamic critical behavior of semi-infinite model C near the special and ordinary transitions is investigated using field theoretic renormalization-group approach. It is shown that the dynamic surface quantities have different critical behavior aginst their bulk analogues and their scaling laws can be expressed entirely in terms of static (bulk and surface) exponents and dynamic exponents. It is found that at the critical point the surface transport coefficient reaches a finite value via a cusplike singularity and the surface-bulk transport coefficient diverges, but the bulk transport coefficient remains finite as that of the infinite model C.