Arbitrary shape text detection is a challenging task due to its complexity and variety, e.g, various scales, random rotations, and curve shapes. In this paper, we propose an arbitrary shape text detector with a boundary transformer, which can accurately and directly locate text boundaries without any post-processing. Our method mainly consists of a boundary proposal module and an iteratively optimized boundary transformer module. The boundary proposal module consisting of multi-layer dilated convolutions will compute important prior information (including classification map, distance field, and direction field) for generating coarse boundary proposals meanwhile guiding the optimization of boundary transformer. The boundary transformer module adopts an encoder-decoder structure, in which the encoder is constructed by multi-layer transformer blocks with residual connection while the decoder is a simple multi-layer perceptron network (MLP). Under the guidance of prior information, the boundary transformer module will gradually refine the coarse boundary proposals via boundary deformation in an iterative manner. Furthermore, we propose a novel boundary energy loss (BEL) which introduces an energy minimization constraint and an energy monotonically decreasing constraint for every boundary optimization step. Extensive experiments on publicly available and challenging datasets demonstrate the state-of-the-art performance and promising efficiency of our method.