This paper is dedicated to the study of viscous compressible liquid-gas two-phase flow model in multi-dimensional spaces $ d\geq2 $. We investigate the global existence of strong solutions to the Cauchy problem in the $ L^p $ critical regularity framework. In comparison with previous results, the high-frequency of dissipative variable $ (\widetilde{P},\widetilde{u}) $ may be bounded in the critical space $ \dot{B}_{p,1}^{d/p}\times\dot{B}_{p,1}^{d/p-1}(p\geq2) $ and the high-frequency of non-dissipative variable $ \widetilde{\rho} $ to be bounded in the $ L^2 $-type Besov space $ \dot{B}_{2,1}^{d/2} $. Moreover, a Lyapunov-type energy argument can be developed, which leads to the time-decay estimates of solutions without additional smallness assumptions.