We present a new constraint on a lepton mixing matrix $V$ from lepton-flavor violating (LFV) processes in supersymmetric standard models with massive neutrinos. Here, we assume Yukawa-coupling unification $f_{ u 3}simeq f_{rm top}$, in which $tau$-neutrino Yukawa coupling $f_{ u 3}$ is unified into top-quark Yukawa coupling $f_{rm top}$ at the unification scale $M_*simeq 3times 10^{16}$ GeV. We show that the present experimental bound on $mu to e gamma$ decay already gives a stringent limit on the lepton mixing (typically $V_{13}<0.02$ for $V_{23}=1/sqrt{2}$). Therefore, many existing neutrino-mass models are strongly constrained. Future improvement of bounds on LFV processes will provide a more significant impact on the models with the Yukawa-coupling unification. We also stress that a precise measurement of a neutrino mixing $(V_{MNS})_{e3}$ in future neutrino experiments would be very important, since the observation of non-zero $(V_{MNS})_{e3}$, together with negative experimental results for the LFV processes, have a robust potential to exclude a large class of SUSY standard models with the Yukawa-coupling unification.
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