We put up a new fast and steady parameter interpolator on the basis of the present various interpolation algorithms. This proposed algorithm has little rate of speed errors than other algorithms and can save much computing time because of its avoiding derivation operations. Quintic curve acceleration/deceleration algorithm (QCAD) is deduced which can improve the flexibility of the CNC machine. By means of the QCAD planning, the demand velocity is maintained high at large of the time and can be smoothly accelerated/decelerated when needed. Therefore, the parameter interpolator with QCAD can meet the CNC dynamic properties to improve the machine quality. In the end, this NURBS interpolator is validated by matlab, which proves this proposed algorithm not only has the advantages of good flexibility and simple implementation procedure, but also has lower time complexity.