In this paper, we study the online heterogeneous transfer (OHT) learning problem, where the target data of interest arrive in an online manner, while the source data and auxiliary co-occurrence data are from offline sources and can be easily annotated. OHT is very challenging, since the feature spaces of the source and target domains are different. To address this, we propose a novel technique called OHT by hedge ensemble by exploiting both offline knowledge and online knowledge of different domains. To this end, we build an offline decision function based on a heterogeneous similarity that is constructed using labeled source data and unlabeled auxiliary co-occurrence data. After that, an online decision function is learned from the target data. Last, we employ a hedge weighting strategy to combine the offline and online decision functions to exploit knowledge from the source and target domains of different feature spaces. We also provide a theoretical analysis regarding the mistake bounds of the proposed approach. Comprehensive experiments on three real-world data sets demonstrate the effectiveness of the proposed technique.