  We present a two-dimensional (2D) Particle-Particle-Particle-Mesh (P$^3$M)
algorithm with an optimized Green function and adaptive softening length for
gravitational lensing studies in N-Body simulations. The analytical form of the
optimized Green function $\hat{G}(\mathbf{k})$ is given. The softening schemes
($S$) are studied for both the PM and the PP calculations in order for accurate
force calculation and suppression of the particle discreteness effect. Our
method is two orders of magnitude more accurate than the simple PM algorithm
with the {\it poor man's} Green function ($\propto1/k^2$) at a scale of a few
mesh cells or smaller. The force anisotropy is also much smaller than the
conventional PM calculation. We can achieve a force accuracy better than 0.1
percent at all scales with our algorithm. When we apply the algorithm to
computing lensing quantities in N-Body simulations, the errors are dominated by
the Poisson noise caused by particle discreteness. The Poisson noise can be
suppressed by smoothing out the particle distribution, which can be achieved by
simply choosing an adaptive softening length in the PP calculation. We have
presented a criterion to set the adaptive softening length. Our algorithm is
also applicable to cosmological simulations. We provide a \textsc{python}
implementation \texttt{P3Mlens} for this algorithm.
