We describe a three-dimensional algorithm for the advancement of the resistive MHD equations in cylindrical geometry with line-tied boundary conditions. This code has been developed to simulate the behavior of solar coronal plasmas. A finitedifference discretization is used for the radial and axial coordinates; a pseudospectral method is used for the azimuthal coordinate. The dependent variables are defined on finite-difference meshes that are staggered with respect to each other to facilitate the application of boundary conditions. The time-advance algorithm features a semi-implicit leapfrog scheme for the wave terms, a predictor-corrector treatment of advection, and an implicit advance of the resistive and viscous diffusion terms. The semi-implicit and implicit operators are inverted using a preconditioned conjugate gradient method. Special care is taken in maintaining the self-adjointness of the discretized operators, so that a fast inversion algorithm applicable to symmetric matrices can be used. By way of illustration, we describe the application of the code to the linear and nonlinear evolution of a kink instability in a twisted flux tube.