Based on Rytov approximation and extended Huygens-Fresnel principle, the analytical expressions for average intensity and scintillation index on target plane in non-Kolmogorov weak turbulence along slant paths were derived, the system efficiency of heterodyne lidar wass given. The system efficiency of heterodyne lidar is examined and the effects of exponent parameter, zenith angle, structure constant, system configurations and telescope aperture on system efficiency are also analyzed.It is shown that when the generalized index is less than 3.2 or greater than 3.8, the system efficiency decreases fast as the index increases. System efficiency decreases with the increase of zenith angle. System efficiency of bistatic configurations is smaller than that of monostatic configurations. With the increase of the telescope aperture, the system efficiency arrives the minimum, and eventually flattens out. In near field, the system efficiency of collimated beam is larger than the other two forms, but in far field the system efficiency of divergent beam is the largestone.