Compared to turbulent combustion in practical combustion devices, a co-flow laminar diffusion flame is the simplest configuration from which the interactions between flow field and reactions can be readily studied. High pressure combustion experiments on the methane/oxygen laminar co-flow diffusion flame are conducted to distinguish combustion states from 0.2 to 4 MPa. The transition combustion state between the steady state and periodical pulsation combustion state is studied quantitatively. The results obtained using a Schlieren device show that the different formation heights of the vortices generated in the jet flame shear layer lead to different combustion states. Based on the combustion pressure and Froude number at the burner exit, the upper and lower limits for the transition combustion state are proposed as Frcr=9.8×10−4(pr−0.012)−1.87 ± 4.0×10−5(pr+0.026)−2.48, respectively. The flame is in the steady combustion state when the flame Fr is smaller than the lower limit of Frcr. When the flame Fr is larger than the upper limit of Frcr, pulsation combustion takes place. For the pulsation combustion state, the relationship between the Strouhal number and Froude number is established as St=0.29×Fr−0.65.