Grating interferometry breast computed tomography (GI-BCT) has the potential to provide enhanced soft tissue contrast and to improve visualization of cancerous lesions for breast imaging. However, with a conventional scanning protocol, a GI-BCT scan requires longer scanning time and higher operation complexity compared to conventional attenuation-based CT. This is mainly due to multiple grating movements at every projection angle, so-called phase stepping, which is used to retrieve attenuation, phase, and scattering (dark-field) signals. To reduce the measurement time and complexity and extend the field of view, we have adopted a helical GI-CT setup and present here the corresponding tomographic reconstruction algorithm. This method allows simultaneous reconstruction of attenuation, phase contrast, and scattering images while avoiding grating movements. Experiments on simulated phantom and real initial intensity, visibility and phase maps are provided to validate our method.