The cross section measurements of a single top quark in association with a Z boson using proton-proton collision data collected by CMS experiment are reported in this thesis. The measurements are performed by analyzing integrated luminosities of 19.7 fb1 and 35.9 fb1 which were collected at 8 TeV and 13 TeV. The measurement are performed within the standard model framework where top quark is produced via the t-channel process. The measurements in three lepton final state, where the W boson from the top quark and the Z boson decay into either electrons or muons, resulting in four possible lepton combinations namely eee, eeµ, µµe, µµµ, are discussed. The final state electrons or muons can also come from from leptonic ⌧ decays, as they are not specifically excluded. The main sources of background to the tZq process are t¯ t production, diboson production (WZ, ZZ), ttV (V = W or Z) and Drell-Yan (DY) production. A simple cut and count technique is used for the cross section measurement. For theps = 8 TeV measurement, a one bin likelihood fit is performed to event yields in each four lepton channels and to the combined channel. The cross section for the combined channel is measured to be (t`+`q) = 18+11 9 (stat)+4 4(syst) fb, where ` stands for electrons, muons and ⌧ leptons, with an observed (expected) significance of 1.81 (0.81) standard deviations. The measured value is compatible with the NLO standard model prediction of 8.2 fb with a theoretical uncertainty of less than 10%. For the second cross section measurement at 13TeV, the signal is extracted by performing a simultaneous binned likelihood fit to yields in the signal and the background enriched control regions. The cross section for the combined channel is measured to be (t`+`q) = 156+47 42(stat)+40 34(syst) fb, which is compatible with the NLO standard model prediction of 94.2 ± 3.1 fb. The measurement is found to be in agreement with the standard model with an observed (expected) significance of 2.81(1.95) standard deviations.