Linear chirp-based underwater acoustic communication has been widely used due to its reliability and long-range transmission capability. However, unlike the counterpart chirp technology in wireless -- LoRa, its throughput is severely limited by the number of modulated chirps in a symbol. The fundamental challenge lies in the underwater multi-path channel, where the delayed copied of one symbol may cause inter-symbol and intra-symbol interfere. In this paper, we present UWLoRa+, a system that realizes the same chirp modulation as LoRa with higher data rate, and enhances LoRa's design to address the multi-path challenge via the following designs: a) we replace the linear chirp used by LoRa with the non-linear chirp to reduce the signal interference range and the collision probability; b) we design an algorithm that first demodulates each path and then combines the demodulation results of detected paths; and c) we replace the Hamming codes used by LoRa with the non-binary LDPC codes to mitigate the impact of the inevitable collision.Experiment results show that the new designs improve the bit error rate (BER) by 3x, and the packet error rate (PER) significantly, compared with the LoRa's naive design. Compared with an state-of-the-art system for decoding underwater LoRa chirp signal, UWLoRa+ improves the throughput by up to 50 times.