Based on the intrinsic randomness of quantum mechanics, quantum random number generators (QRNGs) can produce true random numbers in theory. However, in realistic scenarios, the physical devices of QRNGs may have imperfections or be controlled by some malicious parties, which threatens the security of QRNGs. We experimentally study the security of superluminescent LED (SLED)-based QRNGs under different working conditions. The experimental results show that the output characteristics and performance of the QRNG are affected by the temperature and drive current variations. The higher the drive current of SLED, the greater the influence of temperature variation on the security of the QRNG. Therefore, it is important for the user to choose an appropriate current to drive the QRNG. In addition, our analysis also shows that the QRNG can be more robust by improving the postprocessing method and by monitoring the output optical power as well as the minimum entropy. Thus, this work provides a reference for the standardization of QRNGs.