Adiabatic potential energy surfaces (PESs) for five low lying doublet states (three (2)A(') states and two (2)A(") states) of N(3) are constructed based on 1504 single point calculations at the MRCISD(Q) level using aug-cc-pVTZ basis set. A new strategy is adopted to obtain the final PESs by combining global fits of individual adiabatic PESs and local simultaneous fits of two adiabatic PESs in several conical intersection regions with switching functions. These global fits employ basis functions that satisfy permutational invariance with respect to like nuclei and have rms errors around 2-3 kcal/mol. The special local two-state fits are performed at the cyclic, bent, and linear N(3) conical intersection regions to take account of intrinsic square root behavior of the potentials and to improve the quality of fitting. Stationary points as well as minima on the concial intersections and seams of crossing are located on these PESs and compared with ab initio results. The agreement is satisfactory in most cases. In addition to the construction of adiabatic PESs, diabatization is performed for the 1 (2)A(') and 2 (2)A(') states around their conical intersection at the N(3) bent region. These two diabatic PESs and the diabatic coupling potential have been constructed and reported.