A multi-band terahertz (THz) absorber based on graphene sheet and nanoribbons is proposed and investigated. In the studied frequency range, five absorption peaks are observed, with four originate from lateral Fabry-Perot resonance (LFPR) and one originates from guided-mode resonance (GMR). The LFPR and GMR peaks behave differently when geometric parameters are adjusted, which makes independent tuning possible. When period increases, the GMR peak red shifts and the frequencies of LFPR peaks remain almost unchanged. On the contrary, as nanoribbon width increases, the frequency of GMR remains almost unchanged while that of LFPRs decrease significantly. With increasing top dielectric layer thickness, the LFPR peaks blue shift while the GMR peak red shifts. In addition, the absorber has the merit of multi-band high absorptivity and frequency stability under large angle oblique incidence. The proposed terahertz absorber may benefit the areas of medical imaging, sensing, non-destructive testing, THz communications and other applications.