Energy conservation and accurate angular distribution of radiance are the basic requirements for simulation of radiative transfer processes.Current climate model and operational remote sensing technique demands fast and accurate radiative transfer algorithm.To improve the computational efficiency

the scattering phase function is expanded and truncated as the summation of orthogonal polynomials such as Legendre function.Based on mathematical theory

number of polynomials must agree with streams（number of grids in angular integration） to satisfy the integration conservation

inappropriate truncation of scattering phase function results in considerable errors

especially for strong forward scattering media such as cloud particles and dust aerosol in the atmosphere.The truncated scattering phase function of dust or cloud

which fluctuate with scattering angle

results in false fluctuation in angular distribution of radiance

the fluctuation could be removed through taking huge number terms in expansion of scattering phase function

but energy conservation is broken

radiation flux is wrong and the results are unstable.Based on mathematical and radiative transfer theory

the phenomenon of false fluctuation and the stability of radiative transfer algorithm are analyzed

several fast and accurate methods are compared.Finally

two fast and accurate algorithms

satisfying the energy conservation and using less streams

are given

which is of significance in remote sensing

parameterization of radiative forcing in global climate models

energy budget estimation of the earth-atmosphere system

in particular

the effect of clouds and dust events.