Recently, we have studied new doped alloys CeCo1-xNixIn5 for the first time. The substitution of Ni for Co simply suppresses the superconducting phase without generating antiferromagnetic order. At around the critical concentration x = 0.25, the specific-heat, resistivity, and magnetic susceptibility show non-Fermi-liquid (NFL) behavior suggesting that CeCo1-xNixIn5 for x ≤ 0.25 is located in the proximity of the antiferromagnetic quantum critical point. muSR is a very powerful technique for studying the quantum critical magnetic fluctuations in a microscopic level. In this study, we would like to perform muSR experiments on CeCo1-xNixIn5 in order to further understand the NFL behavior at around x = 0.25. We plan to perform ZF- and LF-muSR experiments to investigate the character of the spin fluctuations under zero and weak magnetic fields.