Accurate prediction of crop yield under the conditions of climate change is crucial to ensure food security. Transformers have shown remarkable success in modeling sequential data and hold the potential for improving crop yield prediction. To understand how weather and meteorological sequence variables affect crop yield, the positional encoding used in Transformers is typically shared across different sample sequences. We argue that it is necessary and beneficial to differentiate the positional encoding for distinct samples based on time-invariant properties of the sequences. Particularly, the sequence variables influencing crop yield vary according to static variables such as geographical locations. Sample data from southern areas may benefit from more tailored positional encoding different from that for northern areas. We propose a novel transformer based architecture for accurate and robust crop yield prediction, by introducing a Customized Positional Encoding (CPE) that encodes a sequence adaptively according to static information associated with the sequence. Empirical studies demonstrate the effectiveness of the proposed novel architecture and show that partially lin- earized attention better captures the bias introduced by side information than softmax re-weighting. The resultant crop yield prediction model is robust to climate change, with mean-absolute-error reduced by up to 26% compared to the best baseline model in extreme drought years.