Recently, multi-interest models, which extract interests of a user as multiple representation vectors, have shown promising performances for sequential recommendation. However, none of existing multi-interest recommendation models consider the Out-Of-Distribution (OOD) generalization problem, in which interest distribution may change. Considering multiple interests of a user are usually highly correlated, the model has chance to learn spurious correlations between noisy interests and target items. Once the data distribution changes, the correlations among interests may also change, and the spurious correlations will mislead the model to make wrong predictions. To tackle with above OOD generalization problem, we propose a novel multi-interest network, named DEep Stable Multi-Interest Learning (DESMIL), which attempts to de-correlate the extracted interests in the model, and thus spurious correlations can be eliminated. DESMIL applies an attentive module to extract multiple interests, and then selects the most important one for making final predictions. Meanwhile, DESMIL incorporates a weighted correlation estimation loss based on Hilbert-Schmidt Independence Criterion (HSIC), with which training samples are weighted, to minimize the correlations among extracted interests. Extensive experiments have been conducted under both OOD and random settings, and up to 36.8% and 21.7% relative improvements are achieved respectively.