The microstructure and tensile properties of a new Ni-based superalloy specially designed for additive manufacture (AM) were investigated under different laser power (LP) conditions. The results measured by X-ray diffraction analysis and scanning electron microscopy show that no cracks are observed in as-deposited alloy, which has typical crystallography orientation and non-equilibrium solidification dendrite/cellular morphology. The elements such as Nb, Si and Ti are enriched in the interdendritic regions, while Al, Cr and Co segregate in the dendritic cores. When the LP is low, the cellular crystals of the alloy are arranged orderly, the primary dendrite arm space (PDAS) is small, the porosity is large, the strength is high and the elongation is low. With the increase of LP, the PDAS increases, the porosity decreases, the strength decreases and the elongation increases. When the LP is elevated further, Marangoni convection effect is enhanced and shows unique impacts, that is, the disordered arrangement of cellular crystals occurs. Then, the PDAS decreases, the porosity increases, the strength increases and the elongation decreases. The smaller PDAS favors the reduction for elements segregation, as well as microstructure refinement and strength improvement. The fitting formula between PDAS and yield strength (YS) was proposed, and the concentric ring patterns inside microstructure were rationalized.