The zero distribution of automorphic L-functions in the critical strip will be discussed. Firstly, we will introduce some results of zeros of Riemann zeta functionζ(s) and Hecke L-function L(s,f). Secondly, the mean value of the argument function ofζ(s) and L(s,f) were considered. By the zero density estimate of L(s,f), the mean value of arg L(s,f) on the critical line in short intervals were given, which improves the work of Sankaranarayanan.