The invention provides a flue gas purification and sulphur recovery system and a process, comprising an adsorber, a desorber, an adsorbent delivery system, a heat energy integrated recovery system and a carbon powder separation and recovery system; meanwhile, suitable processing methods are adopted. The adsorber adopts a single-device dual-section radial staggered moving bed shaped like a reversed u and selective wide spectrum purification; the desorber adopts an axial reflux moving bed to realize the integrated recovery and utilization of the heat energy, regeneration of the adsorbent and the recovery of sulphur resource; the adsorbent adopts dense phase pneumatic conveying, thus leading the system to run continuously and stably; the flue gas purification and the sulphur recovery are realized by the carbon-based column-shaped or sphere-shaped desulfurization and denitration adsorbent. The system effectively integrates the energy-saving, exhaust and consumption reduction and resource recovery and utilization together, and has the advantages of high-effect wide spectrum purification and sulphur resource recovery, good gas distribution, grain movement and low pressure reduction, integrated recovery and utilization of heat energy, delivering the absorbent with no mechanical parts, continuous and stable operation of system, saving equipment investment and operation expense, etc.