We present a novel framework for retrospective dynamic 3D volume reconstruction from a multi-slice MRI acquisition using manifold alignment. K-space data are continuously acquired under free breathing using a radial golden-angle trajectory in a slice-by-slice manner. Non-overlapping consecutive profiles that were acquired within a short time window are grouped together. All grouped profiles from all slices are then simultaneously embedded using manifold alignment into a common manifold space (MS),in which profiles that were acquired at similar respiratory states are close together. Subsequently,a 3D volume can be reconstructed at each of the grouped profile MS positions by combining profiles that are close in the MS. This enables the original multi-slice dataset to be used to reconstruct a dynamic 3D sequence based on the respiratory state correspondences established in the MS. Our method was evaluated on both synthetic and in vivo datasets. For the synthetic datasets,the reconstructed dynamic sequence achieved a normalised cross correlation of 0.98 and peak signal to noise ratio of 26.64 dB compared with the ground truth. For the in vivo datasets,based on sharpness measurements and visual comparison,our method performed better than reconstruction using an adapted central k-space gating method.