Quasars at high redshift can help us to probe the nature of the early universe. Current quasar sample is incomplete in the redshift range from 2.2 to 3 because of the similar quasar colors as stars in the optical band. The main objective of the Chinese LAMOST spectroscopic quasar survey is to discover these missing quasars and provide a quasar sample consisting of 0.3million new quasars brighter than the magnitude limit i = 20.5 in the next 5 years. This will hopefully provide the largest quasar sample for the further studies of AGN physics and cosmology. The improved quasar selection criteria based on the UKIDSS near-IR and SDSS optical colors are introduced, and their advantages in uncovering the missing quasars in the quasar 'redshift desert' (z=2.2 to 3) are demonstrated. We also present some recent discoveries of new quasars from the LAMOST commissioning and other spectroscopic observations. The implications of our study to the ongoing and upcoming large optical and near-IR sky surveys are discussed.