As the introduction of triple-frequency signals in GNSS,the multi-frequency ionosphere correction technology has been fast developing.References indicate that the triple-frequency second order ionosphere correction is worse than the dual-frequency first order ionosphere correction because of the larger noise amplification factor.On the assumption that the variances of three frequency pseudoranges were equal,other references presented the triple-frequency first order ionosphere correction,which proved worse or better than the dual-frequency first order correction in different situations.In practice,the PN code rate,carrier-to-noise ratio,parameters of DLL and multipath effect of each frequency are not the same,so three frequency pseudorange variances are unequal.Under this consideration,a new unequal-weighted triple-frequency first order ionosphere correction algorithm,which minimizes the variance of the pseudorange ionosphere-free combination,is proposed in this paper.It is found that conventional dual-frequency first-order correction algorithms and the equal-weighted triple-frequency first order correction algorithm are special cases of the new algorithm.A new pseudorange variance estimation method based on the three carrier combination is also introduced.Theoretical analysis shows that the new algorithm is optimal.The experiment with COMPASS G3 satellite observations demonstrates that the ionosphere-free pseudorange combination variance of the new algorithm is smaller than traditional multi-frequency correction algorithms. As the introduction of triple-frequency signals in GNSS, the multi-frequency ionosphere correction technology has been fast developing. Note the triple-frequency second order ionosphere correction is worse than the dual-frequency first order ionosphere correction because of the larger noise amplification factor. One of the varities of three frequency pseudoranges were equal, other references presented the triple-frequency first order ionosphere correction, which could make worse or better than the dual-frequency first order correction in different situations. In practice, the PN code rate, carrier-to-noise ratio, parameters of DLL and multipath effect of each frequency are not the same, so three frequency pseudorange variances are unequal. Under this consideration, a new unequal-weighted triple-frequency first order ionosphere correction algorithm, which minimizes the variance of the pseudorange ionosphere-free combination, is proposed in this paper. It is found that conventional dual-frequency first-order correction algorithms and the equal-weighted triple-frequency first order correction algorithm are special cases of the new algorithm. A new pseudorange variance estimation method based on the three carrier combination is also introduced. new algorithm is optimal. The experiment with COMPASS G3 satellite observations demonstrates that the ionosphere-free pseudorange combination variance of the new algorithm is smaller than traditional multi-frequency correction algorithms.