Online travel platforms (OTPs), e.g., bookings.com and Ctrip.com, deliver travel experiences to online users by providing travel-related products. Although much progress has been made, the state-of-the-arts for cold-start problems are largely sub-optimal for user representation, since they do not take into account the unique characteristics exhibited from user travel behaviors. In this work, we propose a State-aware Multi-aspect Interests representation Network (SMINet) for cold-start users recommendation at OTPs, which consists of a multi-aspect interests extractor, a co-attention layer, and a state-aware gating layer. The key component of the model is the multi-aspect interests extractor, which is able to extract representations for the user's multi-aspect interests. Furthermore, to learn the interactions between the user behaviors in the current session and the above multi-aspect interests, we carefully design a co-attention layer which allows the cross attentions between the two modules. Additionally, we propose a travel state-aware gating layer to attentively select the multi-aspect interests. The final user representation is obtained by fusing the three components. Comprehensive experiments conducted both offline and online demonstrate the superior performance of the proposed model at user representation, especially for cold-start users, compared with state-of-the-art methods.