Aiming at the Michaelis-Menten equation with constant coefficients, the fixed point stability of the corresponding difference equation under the control of double fixed time pulse was studied, aiming at expanding the application of the theory in pharmacokinetic system, guiding clinical drug administration strategy and dose control, and describing the changes of hormone level and drug concentration in biological organisms. By constructing the corresponding difference equation, using the stability theory of difference equation, monotonicity, the definition and properties of Lambert W function, the positivity, existence, local stability and global stability of the fixed point were discussed. The global asymptotic stability and conditions of Michaelies-Menten equation with constant coefficients are obtained under the control of double fixed time pulses. According to the results obtained, it is verified that Michaelis-Menten equation with constant coefficient term can describe pharmacokinetic phenomena, and can be in line with biological practical significance.