The atomistic simulation of materials growing in the layer-by-layer mode by the pulsed-laser deposition is a significant challenge mainly due to the short timescales in which the fastest processes on the surface occur together with long periods between pulses. We present a kinetic Monte Carlo algorithm which overcomes the scaling problem by approximation of fast diffusion and by neglecting complex chemical processes. The atomic diffusion is modeled as a two-dimensional gas of material units on each layer. The model is based on a few elementary processes-the condensation of units on the surface, their dissolution back to the gas, and interlayer transport, which can be influenced by the Ehrlich-Schwoebel barrier. With these simplifications, the computational time of the algorithm scales only linearly with the size of the substrate while describing physically relevant growth kinetics. We demonstrate that the simplified model is suitable for simulations of layered growth of thin films in the range from quasicontinuous deposition to low-frequency cases. The model is successfully implemented to provide an alternative explanation of the time evolution of layer coverages by interlayer transport after pulses of deposition experimentally observed during perovskite growth [G. Eres et al., Phys. Rev. B 84, 195467 (2011)PRBMDO1098-012110.1103/PhysRevB.84.195467].