The Majorana neutrino in the type-I seesaw and the pseudo-Dirac neutrinos in the inverse seesaw can have sizable mixings with the light neutrinos in the standard model, through which the heavy neutrinos can be produced at the LHC. In producing the heavy neutrinos, we study a variety of initial states such as quark-quark, quark-gluon and gluon-gluon as well as photon mediated processes. For the Majorana heavy neutrino production, we consider a same-sign dilepton plus dijet as the signal events. Using the recent ATLAS and CMS data at radicals=8TeV with 20.3 and 19.7fb super(-1) luminosities, respectively, we obtain direct upper bounds on the light-heavy neutrino mixing angles. For the pseudo-Dirac heavy neutrino production we consider the final sate with a trilepton plus missing energy as the signal events. Using the recent anomalous multilepton search by CMS at radicals=8TeV with 19.5fb super(-1) luminosity, we obtain upper bounds on the mixing angles. Taking the varieties of initial states into account, the previously obtained upper bounds on the mixing angles have been improved. We scale our results at the 8 TeV LHC to obtain a prospective search reach at the 14 TeV LHC with high luminosities.