Concept lattice and rough set are powerful tools for data analyzing and processing, has been successfully applied to many fields. However, the decision information is incomplete in many information systems. In this paper, the definition of incomplete concept lattice has been proposed, and some relation established between imperfect concept lattice and rough set. As is very important that the paper gives a new attributes reduction algorithm about incomplete concept lattice aims at the matter of the inefficient of reduction strategy based on discernibility matrix. Comparing with the attributes reduction for incomplete concept lattice which based on discernibility matrix, this reduction algorithm, reduces the spatial-temporal complexity.