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In the present work the magnetic susceptibility χ(T,H) and the magnetization M(H,T) were investigated in the temperature range 2–20 K and under magnetic fields 0.01–9 T, and the magnetic phase diagram of Pb3TeCo3V2O14 was determined. The magnetic phase transitions manifest themselves as a slope changes on the χ(T) curves at H ≤ 5 T and as a double peak anomaly on the derivation dχ/dT curves. The anomalies are shifted to lowest temperature and smeared under magnetic field. The anomalies of dχ/dT curves T1(H) and T2(H) is shown on the magnetic phase diagram of Pb3TeCo3V2O14. M(H) curves also demonstrate a slope changes at the phase transitions at T ≤ 8 K. It was found that in the range 2–8.9 K and 0–7.4 T there are two phase-boundary lines between low-(T,H) CS state, intermediate IS state, and high-T paramagnetic (PM) state. The positions of two quantum critical points can be estimated as H1(T→0) ~ 6.3 T and H2(T→0) ~ 7.6 T.