Geometric algebra(GA) is an algebraic language used to describe and calculate geometric problems.Due to its unified expression and coordinate-free geometric calculation, GA has now become an important theoretical foundation and calculation tool in mathematical analysis, theoretical physics, geometry and many other fields.While being widely used in the areas of modern science and technology, GA based analysis is traditionally performed using computer based numerical techniques or symbolic methods.However, both of these techniques cannot guarantee the analysis accuracy for safety-critical applications.The higher order-logic theorem proving is one of the rigorous formal methods.This paper establishes a formal model of GA in the higher-order logic proof tool HOL Light.The proof of the correctness is provided for some definitions and properties including blade, multivector, outer product, inner product, geometric product, inverse, dual, operation rules of basis vector and transform operator.In order to illustrate the practical effectiveness and utilization of this formalization, a conformal geometric model is established to provide a simple and effective way on rigid body motion verification.