A usual way to control time-delay systems is to design a predictive control law. Nevertheless, this theoretically appealing method is difficult to implement numerically in the sense that the implemented closed-loop system can be unstable. This paper paves the way of a new methodology to design a numerically safe approximated control law. It is based on the first quasi-Legendre polynomial coefficients of the control. Described and argued along the paper, several steps lead us to a dynamical controller which is easy to manipulate. After carrying on the design of this so-called quasi-predictive control law, we focused on its stability and robustness properties using fine criteria based on Bessel-Legendre inequality. At the end, by processing simulations and evaluating the performances of the controlled closed-loop on two examples, pros and cons of this new dynamical controller are pointed out.