The invention discloses a synthetic method of a ZSM-51 molecular sieve and the synthesized ZSM-51 molecular sieve. The synthetic method includes: a, mixing tetraethyl ammonium hydroxide, an aluminium source, trimethyl ethyl ammonium bromide, water and a silicon source to obtain a to-be-crystallized mixture; and b, performing first-stage hydrothermal crystallization treatment and second-stage hydrothermal crystallization treatment to the to-be-crystallized mixture obtained in the step a, and washing and drying the obtained crystallized solid. The ZSM-51 molecular sieve synthesized through the synthetic method is large in hydrogen storage adsorption quantity.