Relativistic hydrodynamic simulations play a key role in exploring the QGP bulk property and the QCD phase transition in analyses of high-energy heavy-ion collisions at RHIC and LHC. For the quantitative understanding of the QGP property, hydrodynamic calculation with high-precision is important. Using a Riemann solver based on the two-shock approximation, we construct a new 3+1 dimensional relativistic viscous hydrodynamics code. The new hydrodynamics algorithm has less numerical viscosity, which is important to discuss the physical viscosities at RHIC and LHC. For one of applications of the new hydrodynamics code, we argue the possible development of Kelvin-Helmholtz instability in high-energy heavy-ion collisions.