An imperfect annihilation reaction in a one-dimensional gas is studied to assess the effects of a reaction’s imperfectness on its kinetics. The reaction is initially mapped onto a random walk process with memory. After a master equation for the random walk is obtained, the system is reformulated with the first passage time approach developed in stochastic processes. Consequently, the time dependence of the reactant’s survival probability can be perturbatively found in both nearly perfect and weak reaction limits. Hence, the influence of imperfectness effects on reaction kinetics can be addressed. Although the anomalous kinetics for its diffusive counterpart in a low dimension is well-known, the conditions under which mean-field kinetics might be applicable to the current system are discussed.