Abstract In the paper an alternative method to solve the one-dimensional advective-diffusive equation describing the pollutants transport in river with dead zones is presented. Because very often transport in a small river can be treated as a 1D issue, then instead of numerical solution of the advection-diffusion equation an equivalent approach based on the convolution technique can be used. Consequently, for a given impulse response function the numerical calculations are required to compute a convolution only. The impulse response function is obtained as an analytical solution of the linear advection-diffusion equation for the Dirac delta function imposed as the boundary condition at the upstream end. Therefore, it represents the Gauss distribution and consequently, this approach is unreliable when the dead zones occur. To reproduce an asymmetric distribution of concentration along the channel axis an approximation of analytical impulse response function using the asymmetric Gumbel distribution is proposed. This approach valid for solution of the transport equation with constant coefficients is extended for piecewise constant coefficients. Convolution approach does not produce any numerical dissipation and dispersion errors typically generated by the methods based on the finite difference technique. Validation of the method using the results of field measurements confirmed its effectiveness.