Work on giant dielectric CaCu3Ti4O12 (CCTO) ceramics has been continuously ongoing to obtain materials with a high dielectric constant (ε') and low dielectric loss tangent (tanδ) with both values stable over a wide temperature range. Various methods have been used to modify the materials, such as doping and co-doping with different transition metals at Ca or Cu sites, molar variation of metals (Cu, Ca and Ti), including altering in the methods and conditions of ceramic preparation. In general, the most common problem found in this type of research is that increasing ε' also increases tanδ. Thus, in this work, a one-step polymer pyrolysis (PP) procedure was used to obtain Co2+-doped CaCu3-xCoxTi4.2O12 (x = 0.00, 0.03, 0.05, and 0.07) powders. Then, all powders were sintered to obtain ceramics using two different sintering conditions, 1050 °C for 10 h and 1080 °C for 5 h. The influence of Co2+ ions and sintering conditions on the microstructure, dielectric properties and thermal stability of CaCu3Ti4.2O12 ceramics was investigated. Substitution of Co2+ ions at Cu sites can reduce tanδ values and increase ε' in samples with x = 0.03 and 0.05. However, the tanδ and ε' values were concurrently reduced for x = 0.07. Remarkably, a ceramic with x = 0.07 sintered at 1080 °C for 5 h exhibited very low tanδ(∼0.009) and colossal ε' (∼11551) at 1 kHz and 30 °C, over a broad temperature range (−60 to 150 °C), with stability of Δε' ≤ ±15 %. This ceramic is a suggested candidate material for X8R capacitors. Moreover, increasing the Co2+ doping level could significantly raise the nonlinear coefficient (α) of the ceramics from ∼ 3.48 to 34.30. Additionally, the very high Eb values of ceramics with x = 0.07 sintered at 1050 °C for 10 h and 1080 °C for 5 h were significantly increased by ∼26.34 and 17.45 times, respectively, compared to an undoped ceramic. A widened temperature range where Δε' ≤ ±15 % and tanδ < 0.05 in all ceramics with increasing Co2+ concentration is likely a result of increased grain boundary resistance.