Abstract: We propose a method of dimension reduction for functional data in the framework of effective dimension reduction (EDR), emphasizing on the sparse design where one observes only a few noisy and irregular measurements for some or all of the subjects. The proposed method exploits the general strategy of borrowing strength across the entire sample, and specifically draws the inspiration from multivariate cumulative slicing estimation. This provides an innovative solution to the challenging problem of characterizing the EDR space in the presence of sparse functional data. Our theoretical study reveals the bias-variance tradeoff associated with the regularizing truncation and the decaying structures of the predictor process and the EDR space. The proposed method is conceptually simple, and easy to implement in practice. A simulation study and two real examples are presented to illustrate its superior finite sample performance.