Precise stellar ages of stars are necessary to study the evolution of the Milky Way. The age determination is significantly affected by C and O abundances of stars due to their contribution to the overall metallicity and opacity. On the basis of C and O abundances derived from high-resolution observations, we determine the ages of 148 FGK-type dwarfs in the solar neighborhood by considering C and O enhancements individually. Our results show that using C and O enhancements individually could affect the age determination of the high-α population, especially for stars with [O/α] > 0.2 dex, making them about 1 Gyr younger compared to the results using traditional α-enhanced models. This results in a steeper slope in the age-[α/Fe] relation for the high-α population (changes from 0.0339 ± 0.0075 to 0.0436 ± 0.0086), indicating a higher formation rate. We find no tight relation between age and [α/Fe] or [O/Fe] in the high-α populations. The distribution of space velocity for young α-rich stars shows that they are more likely characterized to the low-α populations.