This paper presents two types of two-dimensional (2-D) adaptive beamforming algorithm which have high rate of convergence. One is a linearly constrained minimum variance (LCMV) beamforming algorithm which minimizes the average output power of a beamformer, and the other is a generalized sidelobe canceler (GSC) algorithm which generalizes the notion of a linear constraint by using the multiple linear constraints. In both algorithms, we apply a 2-D lattice filter to an adaptive filtering since the 2-D lattice filter provides excellent properties compared to a transversal filter. In order to evaluate the validity of the algorithm, we perform computer simulations. The experimental results show that the algorithm can reject interference signals while maintaining the direction of desired signal, and can improve convergent performance.