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In this paper,the solutions of the polynomial system arising from sparse interpolation problems are studied.Exploiting the special structure of the polynomial system,it is proved that: for generic data,all its solutions belong to one equivalence class if the sampling are equally spaced.For some special unequally spaced sampling,we give the upper-bound on the number of solutions of the corresponding polynomial system.Based on the coefficient parameter homotopy method,an efficient algorithm is proposed.Unlike some existing algorithms,the proposed algorithm does not require the assumption of equally spaced sampling or positive weighted coefficients,and it is globally convergent.Preliminary numerical tests show that the new method is promising.