A Large Ion Collider Experiment (ALICE) studies the strong interaction part (Quantum Chromo Dynamics) of the Standard Model at the CERN Large Hadron Collider. ALICE has been designed as a general-purpose heavy-ion detector in order to explore phenomena of strong interacting matter and the quark-gluon plasma (QGP) at extreme values of energy density and temperature in nucleus-nucleus collisions. Results are presented here on the study of J/\(\psi\)production in pp collisions at ALICE. In particular, a measurement of J/\(\psi\) cross-section at \(\sqrt{s}\) = 7 TeV energy has been performed, together with a study of a possible algorithm to separate primary J/\(\psi\) from those coming from decays of B hadrons. The validity of this algorithm in ALICE has been demonstrated using Monte-Carlo samples. The J/\(\psi\) particles have been searched exclusively in the decay channel J/\(\psi\) -> e+e−. The study focused on what would be achievable in a period of early running, with integrated luminosity of L=1.25 nb-1, at a proton-proton centre of mass collision energy of \(\sqrt{s}\) = 7 TeV.