The Poisson-Boltzmann equation governing the electrostatic potential distribution for a charged surface immersed in an electrolyte solution is discussed. The conventional analysis on a constant potential/charge density problem is extended to a mixed boundary condition problem in which a linear combination of potential and its derivative is specified at the charged surface. We show that the difficulty of solving this type of problem can be circumvented by adopting a finite dimension, least square approximation method coupled by a random selection algorithm. The solution procedure provides an efficient and accurate way for the estimation of the unknown coefficients in the general solution of a linearized Poisson-Boltzmann equation. It is essentially independent of the geometry of a charged Surface and the type of boundary condition specified, as long as the general solution can be expressed as a linear combination of harmonic functions.