In the present work the M 1 angular moments model in a moving reference frame is presented for rarefied gas dynamics applications. First of all, the derivation of the angular M 1 moments model in the particles mean velocity frame is introduced. The choice of the mean velocity framework in order to enforce the Galilean invariance property of the model is highlighted. In addition , it is shown that the model rewritten in terms of the entropic variables is Friedrichs-symmetric. Also, the derivation of the associated conservation laws and the zero mean velocity condition are detailed. Secondly, a suitable numerical scheme, preserving the realisable requirement of the numerical solution for the angular M 1 moments model in the mean velocity frame is proposed. Thirdly, some numerical results obtained considering several test cases in different collisional regimes are displayed.