Asymmetric cryptographic schemes, represented by RSA, have been shown to be insecure under quantum computing conditions. Correspondingly, there is a need to study whether the symmetric cryptosystem can still guarantee high security with the advent of quantum computers. In this paper, based on the basic principles of classical slide attacks and Simon’s algorithm, we take LED-like lightweight block ciphers as research objects to present a security analysis under both classical and quantum attacks, fully considering the influence on the security of the ciphers of adding the round constants. By analyzing the information leakage of round constants, we can introduce the differential of the round constants to propose a classical slide attack on full-round LED-64 with a probability of 1. The analysis result shows that LED-64 is unable to resist this kind of classical slide attack, but that attack method is not applicable to LED-128. As for quantum attacks, by improving on existing quantum attack methods we demonstrate a quantum single-key slide attack on LED-64 and a quantum related-key attack on LED-128, and indicators of the two attack algorithms are analyzed in detail. The attack results show that adding round constants does not completely improve the security of the ciphers, and quantum attacks can provide an exponential speed-up over the same attacks in the classical model. It further illustrates that the block cipher that is proved to be safe under classical settings is not necessarily secure under quantum conditions.