The large-amplitude ion-acoustic double layers in a collisionless plasma consisting of isothermal positrons, warm adiabatic ions and two-temperature distribution of electrons are investigated. Using the pseudo-potential approach, an energyintegral equation for the system has been derived which encompasses complete nonlinearity for the plasma system. The existence region of the double layers is analyzed numerically. It is found that for a selected set of physical parameters, the rarefactive double layer exists in the electron-positron-ion plasma. It is found that the existence regime of the double layer is very sensitive to the plasma parameters, e.g. cold electron concentration (μ) and temperature ratio of two electron species (β). An increase in the finite ion temperature ratio increases the amplitude of the rarefactive double layer. To study small-amplitude double layers, we have expanded the Sagdeev potential. In the case of small amplitude, it is found that the amplitude of the double layer increases with increase in ion temperature ratio (σ) and cold electron concentration (μ). However increase in positron concentration (α) and temperature ratio of positrons to electrons (γ) decreases the amplitude of the double layer. The effect of various plasma parameters on the characteristics of the double layers is discussed in detail. The results of the investigation may be helpful to understanding basic plasma characteristics in space.