Abstract Despite tremendous theoretical and experimental progress in continuous variable (CV) quantum key distribution (QKD), the security has not been rigorously established for most current continuous variable quantum key distribution systems that have imperfections. Among these imperfections, intensity fluctuation is one of the principal problems affecting security. In this paper, we provide simple security proofs for continuous variable quantum key distribution systems with intensity fluctuating sources. Specifically, depending on device assumptions in the source, the imperfect systems are divided into two general cases for security proofs. In the most conservative case, we prove the security based on the tagging idea, which is a main technique for the security proof of discrete variable quantum key distribution. Our proofs are simple to implement without any hardware adjustment for current continuous variable quantum key distribution systems. Also, we show that our proofs are able to provide secure secret keys in the finite-size scenario.