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Let L be a lower Hessenberg infinite matrix and denote by(C)-a strictly lower triangular part of the infinite matrix C.The discrete KP Hierarhy is a sequence of discrete non linear latticies of the form dL/dt = [(Lm)-,L],m = 1,2,....For exemple,if L is tridiagonal,then this hierarhy is exactly the Toda latticies hierarhy and the equation ˙L = [(L)-,L] is the known non symmetric form of the Toda equations in Flashka variables.In this case the next equation in the hierarhy ˙L = [(L2)-,L] has a invariant manifold where the main diagonal is zero,this is so called Volterra(Lengmuir)lattice.M.Adler and P.Van Moerbeke [1] proposed a following way to generate a solutions of the discrete KP.Suppose we have an infinite number of weight functions ρ1(x),ρ2(x),ρ3(x),ρ4(x),...Construct a system of monic polynomials p0(x),p1(x),p2(x),p3(x),...,such that deg pk = k and pk(x)is orthogonal to the weights ρ1(x),ρ2(x),...,ρk(x)and p0 = 1.Now if we devellope the polynomial xpn(x)on the base of polynomials p0(x),p1(x),...,pn+1(x)we obtain the coefficients of the n-th row of the Hessenberg matrix L.In the present paper we consider the following system of weights ρ1(x),ρ2(x),...,ρm(x),xρ1(x),xρ2(x),...,xρm(x),x2ρ1(x),...In this case the matrix is band Hessenberg and the polynomials pn(x)are exactly multiple orthogonal polynomials with respect to system of weights ρ1(x),ρ2(x),...,ρm(x).Associated discrete KP equation takes the form ˙L = [(Lm+1)-,L].There is a invariant manifold of variable,where all between diagonal elements of matrix L are zero.Dynamical system in this case is generalized Volterra lattice ˙an = an(∑m j-1 an+j-∑m j-1 an-j).In this talk we will discuss generalized Volterra lattice in connection with multiple orthogonal polynomials(see [2],[3]).