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We present logistic dark energy model (LDEM), where the dark energy density follows a logistic function for the scale factor. The equation of state parameter of dark energy ($w_D$) transitioned from $-1$ in the distant past to its current value of $-0.76$, closely resembling the $\Lambda$CDM model in the early epoch and showing significant deviation in the late phase. The evolution of the deceleration parameter in the LDEM signifies its success in explaining the late-time cosmic acceleration. Model selection based on the Bayesian Information Criterion (BIC), incorporating observations from Type Ia Supernovae (SNe Ia), Observational Hubble data (OHD), and Baryon Acoustic Oscillation (BAO) strongly favors the LDEM over the conventional $\Lambda$CDM model, where BIC is estimated to be $\sim -20$. Incorporating the shift parameter derived from the Cosmic Microwave Background (CMB) data shows competing evidence of the LDEM over the standard $\Lambda$CDM. Remarkably, the Hubble constant ($H_0$) value computed using any of the datasets tends to align closely with the predictions from the Cosmic Microwave Background (CMB), suggesting a need to reconsider the local measurement.