Since most components of sparse multi-path channel (SMPC) are zero, impulse response of SMPC can be recovered from a short training sequence. Though the ordinary orthogonal matching pursuit (OMP) algorithm provides a very fast implementation of SMPC estimation, it suffers from inter-atom interference (IAI), especially in the case of SMPC with a large delay spread and short training sequence. In this paper, an adaptive IAI mitigation method is proposed to improve the performance of SMPC estimation based on a general OMP algorithm. Unlike the ordinary OMP algorithm, a sensing dictionary is designed adaptively and posterior information is utilized efficiently to prevent false atoms from being selected due to serious IAI. Numeral experiments illustrate that the proposed general OMP algorithm based on adaptive IAI mitigation outperform both the ordinary OMP algorithm and the general OMP algorithm based on non-adaptive IAI mitigation.