Over a fieldFof characteristic p = 2, a class of Lie algebrasP(n,m), called non-alternating Hamiltonian algebras, is constructed, wherenis a Positive integer and m=(m1, ⋯,mn) is ann-tuple of positive integers.P(n,m)is a graded and filtered subalgebra of the generalized Jacobson-Witt algebraW(n,m)and bears resemblance to the Lie algebras of Cartan type.P(n,m)is shown to be simple unless m=1 andn< 4. The dimension ofP(n,m)isDifferent from the Lie algebras of Cartan type, allP(n,m)are nonrestrictable. The derivation algebra ofP(n,m)is determined, and the natural filtration ofP(n,m)is proved to be invariant. It is then determined thatP(n,m)is a new class of simple Lie algebras if (n,m) satisfies some condition.