This paper proposes non-orthogonal packet access based on low density signature with phase only adaptive precoding. The proposed access allows multiple user terminals to send their packets simultaneously for implementing massive connectivity, though only one antenna is put on every terminal and on an access point. This paper proposes a criterion that defines the optimum rotation angles for the phase only precoding, and an algorithm based on the steepest descent to approach the optimum rotation angles. Moreover, this paper proposes two complexity-reduced algorithms that converge much faster than the original algorithm. When 6 packets are transmitted in 4 time slots, i.e., overloading ratio of 1.5, the proposed adaptive precoding based on all the proposed algorithms attains a gain of about 4dB at the BER of 10-4 in Rician fading channels.