We present a statistical study on possible association between the unidentified g-ray point sources at the Galactic plane (|b|≤5°) and the Galactic young pulsars with ages of less than 10⁶ yr. Our results suggest that young pulsars may account for the majority of unidentified EGRET sources that are positionally associated with supernova remanants and OB star associations, in such a way that two thirds are young radio quiet pulsars and one third are young radio pulsars. We have studied the variability of these unidentified g-ray sources and found that most of them may be non-variable. Furthermore, we expect that GLAST may detect »80 N₁₀₀ radio pulsars and »1100 N₁₀₀ unidentified g-ray point sources in the Galactic plane with |b|≤5°, where N₁₀₀ is the birth rate of neutron stars in units of 100 years.