The present paper aims to develop a reconstruction method for the right side of a system of ODEs in polynomial form from sparse and irregularly distributed time-series data. This method doesn’t require any additional knowledge about the system and has several steps. The scarcity of the data through the trajectory length is compensated by the artificially generated points using approximating trigonometrical polynomials. Then, we get uniformly spread data points with the step conditioned by the desired accuracy of derivatives approximation in ODEs. This let to further use conventional reconstruction algorithms described in the literature. We test the proposed method on time series data generated from known ODE models in a two-dimensional system. We quantify the accuracy of the reconstruction for the system of ODEs as a function of the amount of data used by the method. Further, we solve the reconstructed system of ODEs and compare the solution to the original time series data. The method developed and validated here can now be applied to large data sets for physical and biological systems for which there is no known system of ODEs.