Coherent X-ray microscopy by phase retrieval of Bragg diffraction intensities enables lattice distortions within a crystal to be imaged at nanometre-scale spatial resolutions in three dimensions. While this capability can be used to resolve structure–property relationships at the nanoscale under working conditions, strict data measurement requirements can limit the application of current approaches. Here, we introduce an efficient method of imaging three-dimensional (3D) nanoscale lattice behaviour and strain fields in crystalline materials with a methodology that we call 3D Bragg projection ptychography (3DBPP). This method enables 3D image reconstruction of a crystal volume from a series of two-dimensional X-ray Bragg coherent intensity diffraction patterns measured at a single incident beam angle. Structural information about the sample is encoded along two reciprocal-space directions normal to the Bragg diffracted exit beam, and along the third dimension in real space by the scanning beam. We present our approach with an analytical derivation, a numerical demonstration, and an experimental reconstruction of lattice distortions in a component of a nanoelectronic prototype device.