We have investigated microstructures in both the antiferroelectric (AFE) and relaxor states of Pb(In1/2Nb1/2)O3 (PIN) with the perovskite structure by a transmission electron microscopy (TEM). Electron diffraction (ED) experiments revealed that the AFE state is characterized as the modulated structure with the modulation vector of q =1/4 1/4 0. High-resolution TEM images clearly show the coexistence of two types of domains consisting of the modulated and the nonmodulated structures with the 100 ∼ 200 nm size. On the other hand, in the relaxor state there appear two types of diffuse scatterings in the ED patterns. One is diffuse spots at the 1/2 1/2 0-type reciprocal positions and the other is diffuse streaks elongating along the <110> direction around the fundamental spots. The real-space TEM images clearly demonstrate the presence of nanodomains with the average size of ∼ 5 nm. These nanodomains in the relaxor state should be responsible for the characteristic dielectric properties.