We performed an improved search for ν_μ → ν_e oscillation with the KEK to Kamioka (K2K) long-baseline neutrino oscillation experiment, using the full data sample of 9.2 × 10¹⁹ protons on target. No evidence for a ν_e appearance signal was found, and we set bounds on the ν_μ → ν_e oscillation parameters. At Δm² = 2.8×10⁻³ eV², the best fit value of the K2K ν_μ disappearance analysis, we set an upper limit of sin² 2Θ_μe < 0.13 at 90% confidence level.