Active matter is a novel class of non-equilibrium systems composed of self-propelled particles such as swarming bacteria and motile colloids. Understanding the diffusion of a passive tracer in active fluids is key to comprehending numerous fundamental biological processes. However, active fluids exhibit exotic properties different from conventional equilibrium materials. In this study, we explore from a theoretical perspective the intriguing enhanced translational diffusion, orders of magnitude stronger than its intrinsic Brownian motion. A theoretical framework based on Langevin equation supplemented with an additional noise term apart from the thermal noise is adopted to study the effects of active fluctuations on particle diffusion. The second noise is referred to as “active noise” arising from the persistent motion of active particles, which is represented by a series of random pulses and described as shot noise for characterizing the run-and-tumble strategy of bacterial motion. The Smoluchowski equation is derived from the Langevin-like model, which allows us to analyze the non-equilibrium evolution of the positions distribution of tracer. Within this approach, the explicit expressions for the mean-square displacement (MSD) and the effective diffusion coefficient D_eff are presented. Our results show how the active noise boosts the mobility of the tracer in terms of the magnitude of active force f_A, the duration time ∆_τ and the average interval time τ. It is found that in the presence of active particles, the tracer exhibits short-time superdiffusion and long-time enhanced diffusion. These anomalous diffusion behaviors become more significant as the augmentation of f_A and ∆_τ, and the superdiffusion factor μ can reach approximately 2. When τ is decreased while f_A and ∆_τ are fixed, the number of active kicks per unit time increases, so the MSD and D_eff of tracer increases. The enhanced diffusion regime is identified in the parameter space diagram. More importantly, we apply our theory to analyze the dynamics of polystyrene and silica bead in suspensions of Escherichia coli. The model proposed in the work successfully reproduces the experimental results with reasonable fitting parameters. Such good agreement demonstrate the validity of our theory which has appropriately addressed the subtle roles of activity to the relevant dynamics.