We introduce a general random walk model that is an extension of the random walk model proposed by Berg. The model can be used to describe a particle's translocation along a polymeric lattice with a nonuniform distribution of obstacles. These obstacles are representative of DNA-bound proteins, of drugs, and of a DNA packing environment. Using this model in the bacteriophage replication process, we show the effects of random obstacles on an ATP-driven particle's translocation along single-stranded DNA. The principal finding is that the average statistical time of the translocation process decreases with the increase of an obstacle's strength. We also find an interesting relation between the average statistical time and the DNA chain length. Our results can be used to explain some physiological phenomena. They show the usefulness of our model in an analysis of the effect of random obstacles on particles' translocation along one-dimensional polymer lattices.