The frequency and time dependence of capacitance of dinaphtho[2,3-b:2',3'-f]thieno[3,2-b]thiophene (DNTT)-based metal-insulator-semiconductor (MIS) capacitors were studied. The frequency spectra show a long and gradual slope over many orders of magnitude in frequency, and the time evolution in the subthreshold region exhibits a logarithmic dependence. These two phenomena are analyzed from a unified point of view on the basis of charge trapping models that were originally developed for Si-based MIS capacitors. The charge trapping model with a Gaussian-distributed surface potential in DNTT successfully reproduces both the frequency and time dependences with the same parameter set.