For enhancing the coupling efficiency between the beam and the photodiode, a special optical taper is proposed for receiving optical signal. Based on the circular symmetric structure of special optical taper, the profile curve equations of it are deduced, including the trigonometric function type, parabolic type and exponential type. Moreover, the coupling efficiencies for special optical tapers with different profile curves are studied. The relationships of incident position, incident angle and coupling efficiency are analyzed. Finally, the comparison of coupling efficiency analytical results is also given.