This paper proposes a method based on baseline-by-baseline convergence to meet the requirements of fast two-dimensional direction-finding of an arbitrary planar array. Firstly， this paper establishes the geometrical and signal models and derives the two-dimensional direction of the arrival formula under the no-phase ambiguity condition. Then， a baseline-by-baseline convergent method is proposed to resolve ambiguity based on the correlation between the baseline template and measured phase difference. Finally， an eight-element arbitrary planar array interferometer verifies the algorithm's effectiveness. The experimental results show that this advanced method can effectively improve the interferometer's two-dimensional direction-finding efficiency by converging the potential angle combination according to the correlation between the phase difference of each baseline template and the measured phase difference.