The invention discloses a low temperature Claus sulfur recovery process. The process mainly comprises a thermal reaction section, a catalytic reaction section and a tail gas incineration section, wherein in a combustion furnace of the thermal reaction section, partial hydrogen sulfide reacts with oxygen to be converted into sulfur dioxide, the hydrogen sulfide and the sulfur dioxide undergo a Claus reaction to generate sulfur, and process gas after sulfur separation enters the catalytic reaction section; in the reactor of each stage of the catalytic reaction section, the hydrogen sulfide and the sulfur dioxide under conventional Claus reaction, catalyst reactivation, sub-dewpoint and sub-solid point low temperature Claus reaction in sequence; after the catalyst reaction section, the tail gas which is subjected to sulfur separation enters the tail gas incineration section, and the tail gas is incinerated and exhausted in the tail gas incineration furnace. The process adopts a lower reaction temperature, contributes to performance of chemical equilibrium towards the direction of sulfur generation, so that conversion rate and recovery rate of sulfur are improved. Moreover, the process has the advantages of simple process flow, relative small equipment and investment, low operation cost and more contribution to environmental protection. The invention also discloses a device for the low temperature Claus sulfur recovery process.