  We generalize the directed percolation (DP) model by relaxing the strict
directionality of DP such that propagation can occur in either direction but
with anisotropic probabilities. We denote the probabilities as $p_{\downarrow}=
p \cdot p_d$ and $p_{\uparrow}=p \cdot (1-p_d)$, with $p $ representing the
average occupation probability and $p_d$ controlling the anisotropy. The
Leath-Alexandrowicz method is used to grow a cluster from an active seed site.
We call this model with two main growth directions {\em biased directed
percolation} (BDP). Standard isotropic percolation (IP) and DP are the two
limiting cases of the BDP model, corresponding to $p_d=1/2$ and $p_d=0,1$
respectively. In this work, besides IP and DP, we also consider the $1/2<p_d<1$
region. Extensive Monte Carlo simulations are carried out on the square and the
simple-cubic lattices, and the numerical data are analyzed by finite-size
scaling. We locate the percolation thresholds of the BDP model for $p_d=0.6$
and 0.8, and determine various critical exponents. These exponents are found to
be consistent with those for standard DP. We also determine the renormalization
exponent associated with the asymmetric perturbation due to $p_d -1/2 \neq 0$
near IP, and confirm that such an asymmetric scaling field is relevant at IP.
