We investigate the phase structure of two-color QCD at both real and imaginary chemical potentials (), performing lattice simulations and analyzing the data with the Polyakov-loop extended Nambu–Jona-Lasinio (PNJL) model. Lattice QCD simulations are done on an lattice with the clover-improved two-flavor Wilson fermion action and the renormalization-group-improved Iwasaki gauge action. We test the analytic continuation of physical quantities from imaginary to real by comparing lattice QCD results calculated at real with the results of an analytic function, the coefficients of which are determined from lattice QCD results at imaginary . We also test the validity of the PNJL model by comparing model results with lattice QCD ones. The PNJL model is good in the deconfinement region, but less accurate in the transition and confinement regions. This problem is cured by introducing the baryon degree of freedom to the model. It is also found that the vector-type four-quark interaction is necessary to explain lattice data on the quark number density.