Muons produced by a short pulse laser can serve as a new type of muon source having potential advantages of high intensity, small source emittance, short pulse duration and low cost. To validate it in experiments, a suitable muon diagnostics system is needed since high muon flux generated by a short pulse laser shot is always accompanied by high radiation background, which is quite different from cases in general muon researches. A detection system is proposed to distinguish muon signals from radiation background by measuring the muon lifetime. It is based on the scintillator detector with water and lead shields, in which water is used to adjust energies of muons stopped in the scintillator and lead to against radiation background. A Geant4 simulation on the performance of the detection system shows that efficiency up to 52% could be arrived for low-energy muons around 200 MeV and this efficiency decreases to 14% for high-energy muons above 1000 MeV. The simulation also shows that the muon lifetime can be derived properly by measuring attenuation of the scintilla light of electrons from muon decays inside the scintillator detector.