We study the Hankel determinant of the generalized Jacobi weight (x − t)γxα(1 − x)β for x ∊ [0, 1] with α, β > 0, t < 0 and . Based on the ladder operators for the corresponding monic orthogonal polynomials Pn(x), it is shown that the logarithmic derivative of the Hankel determinant is characterized by a Jimbo–Miwa–Okamoto σ-form of the Painlevé VI system.