We prove a new algorithm of the linearly equality and inequality constrained nonlinear programming problem. The algorithm not only overcomes the disadvantage of the reduced gradient algorithm, which is only valid for the linear equality constrained nonlinear programming problem, but also has the advantage of lowering the dimension. Further, the algorithm simplifies \textit{K. Ritter}'s algorithm [in: Nonlinear optimization, theory and algorithms, Proc. Int. Summer Sch., Bergamo/Italy 1979, 221-251 (1980; Zbl 0454.90068)]. Its convergence is also proved.