A non-left-right symmetric conformal integrable Toda field theory is c
onstructed. It is found that the conformal algebra for this model is t
he product of a left chiral W-r+1 algebra and a right chiral W-r+1((2)
) algebra. The general classical solution is constructed out of the ch
iral vectors satisfying the so-called classical exchange algebra. In a
ddition, we derived an explicit Wronskian type solution in relation to
the constrained WZNW theory. We also showed that the A infinity limit
of this model is precisely the (B-2, C-1) flOW Of the standard Toda l
attice hierarchy.