The analytical theory of a turbulent scalar, developed in previous papers [Phys. Fluids 28 (1985) 1299; J. Fluid Mech. 217 (1990) 203], is extended to the case of large Prandtl number. The fluctuation character of the least principal rate of strain γ has an important effect upon the scalar spectrum. The scalar variance spectrum in the viscous range isF (k) = 4.472(νε) 1 2 χ k - 1 H (x), x (kk b ) 2 ; H(x) is a dimensionless universal function and is determined by solving numerically the closed spectral dynamical equations. A simple fitting formula of the numerical result isH (x) = 0.7687 exp(-3.79x) + 0.2313exp(-11.13x), which corresponds a two-values fluctuation model of γ. Here ν is the kinematic viscosity, k b (ενμ 2 ) 1 4 is the Batchelor wavenumber, μ is the scalar diffusivity, and ε and χ are respectively the energy and variance dissipation rates.