The vast reserves of natural gas hydrates in offshore areas present significant challenges to development. Surface well construction technology is crucial for the extraction of deepwater natural gas hydrates. To ensure the safety of the subsea wellhead during the drilling process for deepwater natural gas hydrates, a novel conductor suction pile device has been designed, comprising a combination of suction piles and surface conductors. And research has been conducted to investigate the lateral stability characteristics of the conductor suction pile. Drawing upon the pile foundation load-bearing theory and the equilibrium of the differential element, a theoretical analysis model and corresponding governing equations of the conductor suction pile system are established. A solution for a multi-point boundary value problem by simplifying the conductor suction pile system into a two-end free beam is proposed. The governing equations are then converted into a first-order differential equation system, and the four-stage Lobatto IIIa collocation method program for the multi-point boundary value problem is developed and resolved using MATLAB 2023a. Furthermore, a case study of a well in the South China Sea elucidates the effects of wellhead load and seabed soil properties on the lateral load-bearing capacity of the conductor suction pile system, verifying the collocation method’s validity against the results from the finite difference method. After conducting a comparative analysis of the lateral load-bearing performance between conductor suction piles and traditional surface conductors, it is observed that conductor suction piles exhibit lower horizontal displacement and bending moments compared to surface conductors. Therefore, conductor suction piles demonstrate a substantial safety margin. The research findings provide a theoretical basis for the lateral stability of conductor suction piles during deepwater natural gas hydrate drilling. This offers a safe and efficient method for surface well construction in the extraction of natural gas hydrates.