We report on the demonstration of surface-emitted terahertz- (THz-) wave difference-frequency generation from two-dimensional (2D) periodically poled lithium niobate (PPLN). The two orthogonal periodic structures individually compensate for both the phase mismatch of the launched lasers and the generated THz wave. Tunable 1.5-1.8 THz wave generation with a bandwidth of 10-GHz was obtained by use of two 2D PPLN crystals. We also confirmed that THz waves were simultaneously generated into two opposite directions, which suggests the possibility of higher THz-wave output power.