Predictive control recently has gained wide acceptance in the process industry. In practice mostly linear algorithms are applied. Control algorithms considering the nonlinearities of the processes would provide better control performance than the linear algorithms. A new iterative nonlinear predictive control algorithm is presented here based on the quadratic parametric Volterra model. The algorithm uses a GPC-like structure. The control performance is demonstrated by a simulation case study of level control of a two-tank system. The behavior of the new algorithm is compared with other suboptimal nonlinear algorithms.