\textit{R. L. Hardy} proposed a multiquadric (MQ) biharmonic method [Comput. Math. Appl. 19, No. 8/9, 163--208 (1990; Zbl 0692.65003)] for hyperbolic conservation laws; in the present article the authors propose a univariate MQ quasi-interpolation method to solve the hyperbolic equations. The method is tested on the one-dimensional Burgers equation without viscosity and the numerical results are found to be close to the exact solution. The main result is Theorem 2.3 which proves error estimates of order \(O(\lambda h) + O(h^2) + O(\lambda^2 \log h) + \min\{\lambda, {\lambda^2\over h}\}\), where \(h\) is the largest grid size and \(\lambda>0\) is a ``shape parameter''. Reviewer's note: This paper is badly written and I am surprised that the editors at the Journal (Numerical Methods for Partial Differential Equations) allowed such a badly written paper with poor grammar, poor spellings and poor sentence structure to be published in this form.