||This thesis reports the study of the field-induced phase transition in anti-ferromagnet Ba2CuGe2O7. Spin-dynamics (SD) simulations have been con-ducted to study the commensurate-incommensurate(CI) phase transition of the antiferromagnet. Under an increasing applied magnetic field H, the sys-tem undergoes a transition from a 2D spiral state to a spin-flop state, via an intermediate phase which was unclear in previous studies. In the 2D spi-ral phase, the SD simulations yield essentially the same spin structures as the theoretical model does for small enough applied field, but quantitative differences occurs for relative larger field. In the intermediate phase, SD sim-ulations reveal how the spin configuration develops from the spin-spiral state to the spin-flop state as the applied field increases. We study theoretically the ground state of the spin system for both discrete and continuum mod-els. We also prove the plane state is the ground state when H field is small. The properties of spin propagation in two-dimensional plane state are also discussed. Our stability analysis reveals two distinct critical field values Hc(1) and Hc(2).