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This paper considers the improved tan(Ψ(ζ)/2)-expansion method to retrieve the traveling wave solutions of the time-fractional Klien-Fock-Gordon equation. The quadratic case has been discussed for the proposed model. The conformable derivative has been applied on the proposed model for investigating the fractional effects. As a result, abundant traveling wave solutions are found. The method contributes four kinds of solutions which are exponential, hyperbolic, trigonometric and rational function solutions for the aforementioned model. The obtained results are also explained graphically for some particular choices of fractional order α,0<α<1. The fractional effects on solutions have been illustrated through 3D plots and line graphs.