  A discrete random walk method on grids was proposed and used to solve the
linearized Poisson-Boltzmann equation (LPBE) \cite{Rammile}. Here, we present a
new and efficient grid-free random walk method. Based on a modified `` Walk On
Spheres" (WOS) algorithm \cite{Elepov-Mihailov1973} for the LPBE, this Monte
Carlo algorithm uses a survival probability distribution function for the
random walker in a continuous and free diffusion region. The new simulation
method is illustrated by computing four analytically solvable problems. In all
cases, excellent agreement is observed.
