A recent study on anomalous transport in a one-dimensional lattice system with two conserved quantities will be discussed which is based on estimating the correction to the local equilibrium distribution. The local equilibrium distribution along with the correction yields super-diffusive hydrodynamics for energy in the linear response regime. Explicit expression of the super-diffusion equation will be presented. Further, the diffusive correction to the super-diffusive evolution allows one to study a crossover from diffusive to anomalous transport. This crossover is demonstrated numerically through the system size scaling of the stationary current in non- equilibrium steady state prepared by two reservoirs of different temperatures.