The problem of finding integer relation for a set of given real num- bers plays a very important role in many applications in mathematics, physics, computer sciences, etc. One of the most frequently used methods to attack this problem is the PSLQ algorithm, which is known as one of the top ten algorithms in the twentieth century. Because the square root operation is unavoidable in PSLQ in practice, it is difficult to implement the exact PSLQ algorithm in a computer system. Previously, PSLQ was only analyzed in the exact real number arithmetic, but all implementa- tions of PSLQ usually utilize inexact arithmetic. Therefore, it is necessary to establish a theory for numerical PSLQ, which is proposed in this pa- per. In particular, the theory consists of the numerical stability and the complexity on numerical PSLQ.