We consider a mixed finite element method for the numerical discretization of a stationary incompressible magnetohydrodynamics problem in three dimensions with its velocity field is discretized using H1 conforming elements and the magnetic field is approximated by curl-conforming Nédélec elements.Under the assumption that the original model has a unique solution pair,we derive a posteriori error estimates of the incompressible magnetohydrodynamic(MHD)equations with a sharp upper bound.Using these a posteriori error estimates,we construct an adaptive algorithm for computing the solution of 3D magnetohydrodynamics.Numerical experiments are carried out to show the performance of the adaptive finite element method.