The present invention discloses a method of continuously preparing polyether amines and relates to the technical field of hydrogenation and ammoniation (amination) of polyether polyols. Skeletal nickel is used as a catalyst and the polyether polyols are mixed with mixed gas of ammonia and hydrogen to conduct hydrogen ammoniated or amination reaction to obtain the liquid polyether amines. The reaction is conducted in an integrated reactor consisting of a trickle bed reactor and a bubble column reactor and the bubble column reactor is arranged under the trickle bed reactor. The temperature condition of the reaction is 100 DEG C-130 DEG C and the pressure condition is 1-3 MPa. The method realizes relatively high gas-liquid-solid contact ratios at a low moisture content rate, low pressure and temperature and less side reactions, and is conductive for simple device operations. An ammoniation rate is 99.5% or more, a primary amine selectivity is 99.5% or more, the quality of the product is more stable, the quality can be controlled and the investment is less.