We report the multiple magnetic phase transitions and critical behaviour of 2D charge-density wave (CDW) compound TbTe 3 studied by µSR measurements and dc magnetization measurements. Zero-field µSR has shown three magnetic transitions below 7 K. The longitudinal field measurements under 50 G has confirmed the first transition at T N = 6.3 K. Scaling analysis from above T N gives the critical exponent w = 0.63(5), suggesting the Ising 3D antiferromagnetic nature of the ordering, which is likely mediated by the 2D correlations. However, the obtained w = 0.81(5) below T N indicates the ferromagnetic phase, which arises over the multiphase transitions at lower temperatures. Temperature-dependent transverse frequency shift gives a relatively smaller exponent γ = 1.0(1) than the Ising 3D model. The different transitions were also observed by dc magnetization measurements, suggesting two magnetic transitions at 7.4 K and 3.1 K, which correspond to the antiferromagnetic and ferromagnetic phases respectively.