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The phenomenological investigation of noncommutative space-time in thelaboratory frame are presented. We formulate the apparent time variation ofnoncommutativity parameter $\theta_{\mu\nu}$ in the laboratory frame due to theearth's rotation. Furthermore, in the noncommutative QED, we discuss how toprobe the electric-like component  $\overrightarrow{\theta_{E}}=(\theta_{01},\theta_{02},\theta_{03})$ by theprocess $e^-e^+\to\gamma\gamma$ at future $e^-e^+$ linear collider.  We may determine the magnitude and the direction of  $\overrightarrow{\theta_{E}}$ by detailed study of the apparent timevariation of total cross section.  In case of us observing no signal, the upper limit on the magnitude of$\overrightarrow{\theta_E^{}}$ can be determined independently of itsdirection.Comment: 12 pages, 7 figures, typos are corrected, one graph have been added  in figure

Probing noncommutative space-time in the laboratory frame