In this paper, a novel full-duplex non-coherent (FD-NC) transmission scheme is developed for massive multiple-input multiple-output (mMIMO) systems using analog beamforming (ABF). We propose to use a structured Grassmannian constellation for the non-coherent communications that does not require channel estimation. Then, we design the transmit and receive ABF via the slow time-varying angle-of-departure (AoD) and angle-of-arrival (AoA) information, respectively. The ABF design targets maximizing the intended signal power while suppressing the strong self-interference (SI) occurred in the FD transmission. Also, the proposed ABF technique only needs a single transmit and receive RF chain to support large antenna arrays, thus, it reduces hardware cost/complexity in the mMIMO systems. It is shown that the proposed FD-NC offers a great improvement in bit error rate (BER) in comparison to both half-duplex non-coherent (HD-NC) and HD coherent schemes. We also observe that the proposed FD-NC both reduces the error floor resulted from the residual SI in FD transmission, and provides lower BER compared to the FD coherent transmission.