The diffusive behavior in a spinel-type Li+ ion battery material, Li[Ni1/2Mn3/2]O4, has been studied with positive and negative muon spin rotation and relaxation (μ±SR) measurements in the temperature range between 200 and 400 K using a powder sample. The implanted μ+ locates at an interstitial site near O2- ion so as to form a O-H like bond, while the implanted μ- is mainly captured by an oxygen nucleus, resulting in the formation of muonic oxygen. This means that local magnetic environments in Li[Ni1/2Mn3/2]O4 were investigated from the two different sites in the lattice, i.e., one is an interstitial site for μ+SR and the other is an oxygen site for μ-SR. Since both μ+SR and μ-SR detected an increase in the fluctuation rate of a nuclear magnetic field for temperatures above 200 K, the origin of this increase is clearly confirmed as Li diffusion. Assuming a random walk process with the hopping of thermally activated Li+ between a regular Li site and the nearest neighboring vacant octahedral sites, a self-diffusion coefficient of Li+ was found to range above 10-11 cm2/s at temperatures above 250 K with an activation energy of about 0.06 eV.