In this paper, we consider a class of first-order hyperbolic distributed parameter systems. Our focus is on the design of a new class of model predictive control schemes using a quasi-Shannon wavelet basis. First, the first-order hyperbolic distributed parameter system is transformed into an equivalent system using collocation techniques for the approximation of spatial derivatives and Euler forward difference method for the approximation of the time component. Then, a model reduction method is applied to obtain a reduced-order system on which a nonlinear model predictive controller is designed through solving a nonlinear quadratic programming problem with input constraints. For illustration, the temperature control of a flow-control long-duct heating system is considered to be an example. A comparative simulation study is conducted to demonstrate the effectiveness of the proposed method.