Reconfigurable Intelligent Surface (RIS) is considered as an energy-efficient solution for future wireless communication networks due to its fast and low-cost configuration. In this letter, we consider the estimation of cascaded channels in a double-RIS aided massive multiple-input multiple-output system, which is a critical challenge due to the large number of antennas equipped at the base station and passive RIS elements. To tackle this challenge, we propose a skip-connection attention (SC-attention) network that utilizes self-attention layers and skip-connection structure to improve the channel estimation performance from the noisy pilot-based observations. Simulation results compare the proposed SC-attention network with other benchmark methods and show that SC-attention network can effectively improve the accuracy performance on normalized mean square error (NMSE) for cascaded links in a double-RIS aided system.