We calculate the tree-level contributions to electroweak observables in the context of a simple group little Higgs model with approximate [SU(4)/SU(3)] global symmetry and with anomaly-free embedding of the SU(2)L⊗U(1)Y electroweak gauge group into SU(4)L⊗ U(1)X . By performing a global fit to 22 observables we bound the Z−Z ′ mixing angle θ, and obtain lower bounds on the mass of the corresponding physical new neutral gauge boson Z2, and on the parameter scale f associated to the SU(4) → SU(2) breaking. Electroweak precision data produce the constraints 0 ≤ θ ≤ 1.33×10−3, MZ2 ≥ 1.23 TeV, and f ≥ 1.56 TeV.