We consider chiral Schwinger model with Faddeevian anomaly, and carry out the quantization of both the gauge-invariant and non-invariant version of this model has been. Theoretical spectra of this model have been determined both in the Lagrangian and Hamiltonian formulation and a necessary correlation between these two are made. BRST quantization using BFV formalism has been executed which shows spontaneous appearance of Wess-Zumino term during the process of quantization. The gauge invariant version of this model in the extended phase space is found to map onto the physical phase space with the appropriate gauge fixing condition.