Supervised classification methods have been widely used in the hyperspectral remote sensing image analysis. However, they require a large number of training samples to guarantee good performance, which costs a large amount of time and human labor, motivating researchers to reuse labeled samples from the mass of pre-existing related images. Transfer learning methods can adapt knowledge in the existing images to solve the classification problem in new yet related images, and have drawn increasing interest in the remote sensing field. However, the existing methods in the RS field require that all the images share the same dimensionality, which prevents their practical application. This paper focuses on the transfer learning problem for heterogeneous spaces where the dimensions are different. We propose a novel iterative reweighting heterogeneous transfer learning (IRHTL) framework that iteratively learns a common space for the source and target data and conducts a novel iterative reweighting strategy to reweight the source samples. In each iteration, the heterogeneous data are first mapped into a common space by two projection functions based on a weighted support vector machine. Second, based on the common subspace, the source data are reweighted by using the iterative reweighting strategy and reused for the transferring, according to their relative importance. Experiments undertaken on three data sets confirmed the effectiveness and reliability of the proposed IRHTL method.