This paper presents a framework for a strapdown Inertial Navigation System (INS) algorithm design by using Lie group and Lie algebra. The general way to solve Lie group differential equations is introduced. Investigations reveal that this general Lie group method provides a simpler unified way to solve differential equations involving direction cosine matrix, quaternion and dual quaternion, which are widely used in INS algorithm design. Furthermore, we also present a new INS algorithm based on the Special Euclidean group SE(3) under the guidelines of Lie group method. Analyses show that SE(3) algorithm has the same accuracy as a dual quaternion algorithm, this is also justified by numerical simulations. Though the SE(3) algorithm has no improvements in accuracy, the general Lie group method used in the design process shows its brevity and uniformity.