We construct the W 1+∞ 3-algebra and investigate the relation between this infinitedimensional 3-algebra and the integrable systems. Since the W 1+∞ 3-algebra with a fixed generator W 0 0 in the operator Nambu 3-bracket recovers the W 1+∞ algebra, it is natural to derive the KP hierarchy from the Nambu-Poisson evolution equation. For the general case of the W 1+∞ 3-algebra, we directly derive the KP and KdV equations from the Nambu-Poisson evolution equation with the different Hamiltonian pairs. We also discuss the connection between the W 1+∞ 3-algebra and the dispersionless KdV equations. Due to the Nambu-Poisson evolution equation involves two Hamiltonians, the deep relationship between the Hamiltonian pairs of KP hierarchy is revealed. Furthermore we give a realization of W 1+∞ 3-algebra in terms of a complex bosonic field. Based on the Nambu 3-brackets of the complex bosonic field, we derive the (generalized) nonlinear Schrödinger equation and give an application in optical soliton.