A physical model for a two-level atom simultaneously coupled to multiple Bosonic reservoirs is investigated. The explicit expression of quantum speed limit is obtained. Analysis shows that as long as the number of reservoirs satisfies certain conditions, whether it is strong coupling or weak coupling, the system will show a non-Markov effect. Numerical simulation shows that the non-Markovian effect of the system increases with the increasing of reservoir number. Further investigation shows that the stronger the non-Markov effect is, the faster the evolution acceleration of quantum system will be.