In this paper an efficient approach is presented for a kind of feed network for microstrip antenna arrays. Both electric and magnetic dyadic Green's functions in the cylindrical coordinate for the radial waveguide are given for efficient numerical calculations. The validity and efficiency of this approach are confirmed by the comparison of the calculated results and data published in the literature. Then, a more complex feed network used by Nakano et al  and Luk et al.  is analyzed and is optimized to obtain a new dimension of this feed network having a uniform current distribution for the array elements. Furthermore, a new kind of topology of the feed network is proposed, which is more easily optimized as a feed network having a uniform current distribution for the array elements.