Based on the two-variable polynomial model of magnetization, magnetic entropy change of bilayered manganites with $327$-structure and its scaling behaviour with respect to applied magnetic fields are investigated. Its found that the Curie temperature, which is defined as the point at which the partial derivative of magnetization with respect to temperature reaches its maximum, is different from the temperature of peak magnetic entropy change. Thus a mean-field model can not apply to this kind of manganites. In contrast to what has been found in manganites with the $113$-structure, the scaling behaviour at the Curie temperature in manganites with $327$-structure is much different from that at the temperature of peak magnetic entropy. Its also found that the temperature dependence of the scaling exponent under weak fields is distinct from that under strong fields.This difference is attributed to an crossover from one-step transition under weak fields to two-step transition under strong fields.
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