Limitation of synchronizing speed is a key feature for finite time synchronization of complex networks. We studied such limitations as coupling strength tends to infinity for networks with Lorenz oscillator as nodes under conditions that nodes were coupled in different ways. It was found that if nodes are coupled by only one state variable, coupling by second variable has the highest synchronizing speed. If nodes are coupled by two state variables, coupling by second and third variables has the highest synchronizing speed. If nodes are coupled by all three variables, the limitation of synchronizing speed will approach infinity.