The invention provides a preparation method of a Cu-SSZ-13 molecular sieve based catalyst. The preparation method comprises the following steps of adding sodium aluminate, sodium hydroxide, a silica solution, copper sulfate, tetraethylenepentamine and an organic template agent to deionized water, and performing stirring so as to obtain gel; and performing a reaction in a reaction kettle, then performing cooling, performing centrifugal filtration, performing washing, performing drying, and performing calcining so as to obtain the Cu-SSZ-13 molecular sieve based catalyst. The method disclosed by the invention is simple in technology, low in cost, energy-saving, and environmentally-friendly. Use of a copper salt solution ion exchange and calcining technology many times is avoided, and the defect that a conventional technology needs performing later-period ion exchange so as to reduce content of active components is overcome. The silica alumina ratio of the Cu-SSZ-13 molecular sieve based catalyst prepared by the method disclosed by the invention is adjustable within the range of 7.9- 26.7, and the percentage by mass of copper is in the range of 0.47 -8.6wt%, excellent NH3-SCR catalytic activity, water thermal stability, alkali metal poisoning resistance and noble metal poisoning resistance can be kept in a wide-temperature window.