Federated Learning (FL), a privacy-oriented distributed ML paradigm, is being gaining great interest in Internet of Things because of its capability to protect participants data privacy. Studies have been conducted to address challenges existing in standard FL, including communication efficiency and privacy-preserving. But they cannot achieve the goal of making a tradeoff between communication efficiency and model accuracy while guaranteeing privacy. This paper proposes a Conditional Random Sampling (CRS) method and implements it into the standard FL settings (CRS-FL) to tackle the above-mentioned challenges. CRS explores a stochastic coefficient based on Poisson sampling to achieve a higher probability of obtaining zero-gradient unbiasedly, and then decreases the communication overhead effectively without model accuracy degradation. Moreover, we dig out the relaxation Local Differential Privacy (LDP) guarantee conditions of CRS theoretically. Extensive experiment results indicate that (1) in communication efficiency, CRS-FL performs better than the existing methods in metric accuracy per transmission byte without model accuracy reduction in more than 7% sampling ratio (# sampling size / # model size); (2) in privacy-preserving, CRS-FL achieves no accuracy reduction compared with LDP baselines while holding the efficiency, even exceeding them in model accuracy under more sampling ratio conditions.