A self-consistent three-dimensional (3D) mathematical model was developed to predict the crystal growth and microstructure formation in the laser powder deposition (LPD) of single-crystal (SX) superalloy. The effects of the governing processing parameters of LPD, i.e. laser power, scanning speed, powder feeding rate on the crystal growth and microstructure formation were studied systemically through the mathematical modeling and experimental approaches. Experiments with SX nickel-based superalloy Rene N5 were conducted to verify the computational results. The results indicate that the processing parameters have a profound influence on the molten pool shape and in turn the resulted epitaxial crystal growth patterns in the deposited bead. The height ratio (height of epitaxial columnar dendrite to total height of deposit) of the epitaxial columnar dendrite along the 001/〈100〉 crystallographic orientation increases up to 52% with the increase of the scanning speed, but decreases down to 42% with the increase of laser power. The simulation results and experimental results of the epitaxial height ratio agree reasonably well. With the optimized processing parameters, the laser deposited multi-layer SX sample with continuous growth columnar dendrite microstructure is demonstrated.