This paper considers plasma charging on the lunar surface with a focus on photoelectron sheath. The plasma species includes ambient solar wind (protons and electrons) and photoelectrons emitted from the illuminated lunar surface. This work is motivated by the high computational cost associated with uncertainty quantification (UQ) analysis of plasma simulations using high-fidelity fully kinetic models. In this paper, we study the photoelectron sheath near the lunar surface with a focus on effects of variables of uncertainty (such as the ambient electron density or photoelectron temperature) on the plasma environment. A fully kinetic 3-D finite-difference (FD) particle-in-cell (PIC) code is utilized to simulate the plasma interaction near the lunar surface and the resulting photoelectron sheath. For the uncertainty quantification analysis, this PIC code is treated as a black box providing high-fidelity quantities of interest, which are also used to construct efficient reduced-order models to perform UQ analysis. A 1-D configuration is first studied to demonstrate the procedure and capability of the UQ analysis. The rest of the paper is organized as follows. Section III presents the analytic and numerical solutions of the 1-D photoelectron sheath. Verification and validation of the FD-PIC code for photoelectron sheath solution is shown. Section IV describes the Kriging model and the uncertainty quantification approach. Section V discusses the UQ analysis of the 1-D photoelectron sheath. The conclusion is given in Section VI.