The present invention discloses a formate dehydrogenase mutant with improved enzyme activity and stability and a construction method thereof, which belongs to the technical field of genetic engineering. The mutant of the present invention is obtained by mutating alanine at a 10th site to cysteine based on the amino acid shown in SEQ ID NO. 2. The specific enzyme activity of the mutant enzyme obtained by the present invention is improved by 1.3 times compared with that before the mutation, a half-life period (t1/2) at 60° C. is increased by 6.8 times compared with that in the mutation period, the copper ion tolerance is increased by 30 times compared with that before the mutation, and when pH is 4, the stability is improved by 2.0 times, and the catalytic efficiency is increased by 1.4 times. The present invention shows that an amino acid residue at a 10th site is mutated to the cysteine which forms a correct disulfide bond with a cysteine residue at a 30th site of the natural formate dehydrogenase, so that the stability and the catalytic efficiency of the enzyme are improved, and the industrial application potential of the enzyme is improved.