Cell-free Massive MIMO (mMIMO) is envisaged to be a next-generation technology beyond 5G with its high spectral efficiency and superior spatial diversity as compared to that of conventional MIMO technology. The main principle is that many distributed access points (APs) cooperate to simultaneously serve all the users within the network without creating cell boundaries. This paper considers the uplink of a cell-free mMIMO system utilizing the radio stripe network architecture. We propose a novel sequential processing algorithm with normalized linear minimum mean square error (N-LMMSE) combining at every AP. This algorithm enables interference suppression in cell-free mMIMO while keeping the cost and front-haul requirements low. The spectral efficiency of the proposed algorithm is computed and analyzed. We conclude that it provides an attractive trade-off between low front-haul requirements and high spectral efficiency.