Long-range (LoRa) communication has attracted much attention recently due to its application for many Internet of Things applications. However, one of the key problems of the LoRa technology is it is vulnerable to noise/interference due to the use of only up-chirp signals during modulation. In this paper, to solve this problem, unlike the conventional LoRa modulation scheme, we propose a modulation scheme for LoRa communication based on joint up- and down-chirps. A fast Fourier transform (FFT) based demodulation scheme is devised to detect modulated symbols. To further improve demodulation performance, a hybrid demodulation scheme, comprised of FFT and correlation-based demodulation is also proposed. The performance of the proposed scheme is evaluated through extensive simulation results. Compared to the conventional LoRa modulation scheme, we show that the proposed scheme exhibits over 3 dB performance gain at bit error rate of 10^-4.