In this study, we have demonstrated the expansion history of an axially symmetric Bianchi type-I model of the universe. Our model as of now presents an accelerating universe, which had been in the decelerating phase in the past. Roles of the two crucial Hubble H(z) and deceleration q(z) parameters are examined. The energy parameters of the universe are estimated with the help of the latest observational Hubble data (46-data points) and Pantheon data (the latest compilation of SNIa with 40 binned in the redshift range 0.014 ≤ z ≤ 1.62). We also discuss the stability analysis of the model by state finder diagnosis. The analysis reveals that in late time, the model is a quintessence type and points towards the ΛCDM model. Our developed model agrees with observational findings in a proper way. We have discussed some of the physical aspects of the model.