This paper proposes and investigates several deep neural network (DNN)-based score compensation, transformation and calibration algorithms for enhancing the noise robustness of i-vector speaker verification systems. Unlike conventional calibration methods where the required score shift is a linear function of SNR or log-duration, the DNN approach learns the complex relationship between the score shifts and the combination of i-vector pairs and uncalibrated scores. Furthermore, with the flexibility of DNNs, it is possible to explicitly train a DNN to recover the clean scores without having to estimate the score shifts. To alleviate the overfitting problem, multi-task learning is applied to incorporate auxiliary information such as SNRs and speaker ID of training utterances into the DNN. Experiments on NIST 2012 SRE show that score calibration derived from multi-task DNNs can improve the performance of the conventional score-shift approch significantly, especially under noisy conditions.