In recent years, there has been a growing focus on developing Low Power Wide Area Network (LPWAN) protocols, especially within the LoRa research community. However, the research community for NB-IoT, another crucial LPWAN technology, has not experienced comparable expansion due to the absence of a functional and adaptable software-defined radio (SDR) implementation. To address this gap, we present SoftNB, the first fully functional physical layer SDR implementation for NB-IoT. SoftNB conforms to the latest 3GPP standards and features an efficient and effective signal processing pipeline to mitigate time, frequency, and phase offsets during transmission and reception. Additionally, SoftNB is compatible with various SDR platforms, including USRP, HackRF One, and RTL-SDR Dongle. Extensive evaluations of SoftNB demonstrate its superior performance. Compared to the state-of-the-art baseline, SoftNB achieves an 8× reduction in Block Error Rate (BLER) when the number of repetitions is set to 4 at a distance of 450 meters.