In the condition assessment process of power transformer, the randomness and uncertainty coexists, it is difficult for the cloud model described by membership degree to portray the non-membership degree and hesitancy degreed. An assessment method based on intuitionistic normal cloud model with optimal variable weights is proposed, which realizes the translation form qualitative to quantitative scale by using a compound two tuple method and optimal variable weights of each state quantity, accordingly. An intuitionistic normal cloud model with reasonable digital characteristics is proposed to describe the fuzziness, randomness and hesitation in the process of insulation condition assessment. Then, the whole insulation condition and fault types of transformer are determined via cloud aggregation. Local case study proves the feasibility and the effeteness of the strategy proposed, which provides a new method for online insulation condition maintenance of power transformer.