To improve the flow characteristics of tandem cascades on design and off design incidence angle and increase the stable operation range, a multi-objective optimization methodology based on CO-kriging and parallel multi-point sampling strategy is presented to realize multi-objective optimization of tandem cascades. Co-kriging model created by a greater quantity of low-fidelity samples coupled with a small amount of high-fidelity samples is introduced to reduce the compute cost of multi-objective optimization problems. The prediction performances of Co-kriging are much better than those of Kriging based on two numerical examples. The multi-point sampling strategy based on the fuzzy c-means clustering method can realize a good balance between exploitation known regions and exploration unknown regions for selecting new samples to update the Co-kriging. And the multi-objective optimization methodology can obtain the approximate Pareto frontier at a less compute cost and was validated by applying it to achieve the multi-objective optimization of a high-turning tandem cascade. After optimization, for the optimal tandem cascade, the static pressure ratio is higher and the total pressure loss coefficient is smaller at all incidence angle conditions. At inlet Mach number of 0.7, when incidence angle is −6° and 3°, the total pressure loss coefficient is respectively decreased by 21% and 35%. Tandem cascades with a high PP (about 0.92) and a negative KBB (about −6°) can realize good flow performances on design and off design incidence angle. And a large TR can improve the flow characteristics of tandem cascades on design and off design incidence angle and increase the stable operation range.