Efficient and accurate numerical methods are very crucial to tackle the strongly correlated quantum lattice systems.In this talk,I shall discuss two novel tensor network-based algorithms that were developed recently by us,as well as their successful applications to quantum spin lattice models.In the first part,I will describe briefly the strategy of the linearized tensor network renormalization group (LTRG) approach and application to the spin-1 bond-alternating Heisenberg spin chain in longitudinal and transverse magnetic fields.In the second part,I shall give an overall description of modified Tucker decomposition for tensor network and a new approach dubbed as the optimized decimation of tensor networks with super-orthogonalization (ODTNS) algorithm for two-dimensional quantum lattice systems,and its application to a frustrated bilayer honeycomb Heisenberg model,where a gapless quantum spin liquid phase is identified.