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In this work we further study the hierachical reconstruction (HR) (Liu, Shu, Tadmor and Zhang, SINUM 07) for discontinuous Galerkin method (DG) on triangular meshes.A WENO-type linear reconstruction is developed on each hierachical stage, in which the weights are essentially independent of the mesh shape and thus are relatively simple.This linear reconstruction is better at reducing the abrupt shift of stencils (which may cause degeneration of accuracy) for unstructured meshes and has better performance in resolving contacts.Several new phenomena and techniques are found during the research.For example, the linear DG method tends to have smaller and smaller CFL number as the order goes higher and higher.