An alternative approach to prevent spurious behavior caused by conventional shock-capturing schemes when solving stiff detonation wave problems is introduced. In engineering research of detonation waves, conventional shock-capturing schemes usually encounter difficulties in identifying the location of the detonation front because the discontinuous solution is smeared. To overcome this excessive numerical dissipation with traditional discretized schemes used in nonreacting high-speed compressible flow, a shock-capturing scheme is introduced in which, besides the linear function constructed in the monotone upstream-centered schemes for conservation law (MUSCL) scheme, a steplike tangent of hyperbola for interface capturing (THINC) function is also employed in the reconstruction process. The final reconstruction function is determined using the boundary variation diminishing (BVD) algorithm, which reduces significantly the numerical dissipation around discontinuities. One- and two-dimensional comparative numerical tests of stiff detonation wave problems were conducted with the fifth-order weighted essentially nonoscillatory and MUSCL-THINC-BVD schemes, demonstrating that the latter scheme reproduces the correct position of detonation waves with improved resolution, whereas the former scheme, despite the higher order, produces spurious waves. Compared with other methods, which, by accepting smeared-out discontinuities profiles, require extra treatments, the current method obtains the correct but also sharp detonation front by fundamentally reducing numerical dissipation errors in shock-capturing schemes.