  We investigate the quantization of the bosonic string model which has a local
U(1)_V * U(1)_A gauge invariance as well as the general coordinate and Weyl
invariance on the world-sheet. The model is quantized by Lagrangian and
Hamiltonian BRST formulations {\'a} la Batalin, Fradkin and Vilkovisky and
noncovariant light-cone gauge formulation. Upon the quantization the model
turns out to be formulated consistently in 26+2-dimensional background
spacetime involving two time-like coordinates.
