a b s t r a c tIn this paper, by virtue of using the linear combinations of the shifts of f (x) to approximate the derivatives of f (x) and Waldron's superposition idea (2009), we modify a multiquadric quasi-interpolation with the property of linear reproducing to scattered data on onedimensional space, such that a kind of quasi-interpolation operator L r+1 f has the property of r + 1(r ∈ Z, r ≥ 0) degree polynomial reproducing and converges up to a rate of r + 2.There is no demand for the derivatives of f in the proposed quasi-interpolation L r+1 f , so it does not increase the orders of smoothness of f . Finally, some numerical experiments are shown to compare the approximation capacity of our quasi-interpolation operators with that of Wu-Schaback's quasi-interpolation scheme and Feng-Li's quasi-interpolation scheme.