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Magnetic properties of Na2Co2TeO6 were studied comprehensively employing magnetic susceptibility, heat capacity, magnetization, electron spin resonance (ESR) as well as density functional theory calculations. The compound orders antiferromagnetically with Neel temperature ~26 K, however both antiferromagnetic and ferromagnetic interactions are found to be present being in delicate balance and resulting in a complicated quantum ground state. The magnetic susceptibility confirmed by specific heat data distinctly displays two-step successive phase transition at low temperature with TN ~ 26 and T2 ~ 13 K. The magnetization curves revealed a field-induced (spin-flop type) transition below T2 temperature in relatively weak magnetic fields of ~0.3 T at T=2 K. Electron spin resonance (ESR) spectra show a single strongly anisotropic absorption line attributed to Co2+ ion in octahedral coordination with almost temperature independent effective g-factor g=2.400.05. In the paramagnetic phase the temperature dependence of the magnetic susceptibility nicely follows the Curie-Weiss law with a positive value of Weiss temperature of about 5 K, indicating a predominance of ferromagnetic correlations and effective magnetic moment eff 6.9 B/f.u., which is in reasonable agreement with theoretically estimated value assuming high-spin state for Co2+ ions (S = 3/2). Spin exchange interactions have been obtained from GGA+U calculations. Theoretical calculations show that the interlayer interaction is ferromagnetic, while the intralayer interactions lead to the stripe antiferromagnetic structure within each layer with preferred spin orientation to be parallel to c-axis. Based on the results of magnetic and thermodynamic studies in applied fields up to 9 T we propose the magnetic phase diagram in agreement with our experimental findings. Rich variety of the anomalies in magnetic properties makes quasi 2D compound Na2Co2TeO6 an interesting system to investigate the multiple phase transitions triggered by complex interplay between competing exchange interactions on honeycomb-lattice.