Abstract: In Euclidean 3-space, a quadric surface is the zero set of a quadratic equation in three variables. Its projective closure can be given as the closure of the image of a rational parametrization where P maps the parameters to the tuple and a, b, c, d are linearly independent quadratic polynomials, with gcd(a, b, c, d)=1. This paper provides an algorithm to classify the type of quadric surface, and identify the normal forms solely based on the parametrization of the quadric surface.