We present a novel Lyman alpha (Ly \ensuremathα) radiative transfer code, SEURAT (SPH scheme Extended with Ultraviolet line RAdiative Transfer), where line scatterings are solved adaptively with the resolution of the smoothed particle hydrodynamics (SPH). The radiative transfer method implemented in SEURAT is based on a Monte Carlo algorithm in which the scattering and absorption by dust are also incorporated. We perform standard test calculations to verify the validity of the code; (i) emergent spectra from a static uniform sphere, (ii) emergent spectra from an expanding uniform sphere, and (iii) escape fraction from a dusty slab. Thereby, we demonstrate that our code solves the \Ly\ \ensuremathα radiative transfer with sufficient accuracy. We emphasize that SEURAT can treat the transfer of \Ly\ \ensuremathα photons even in highly complex systems that have significantly inhomogeneous density fields. The high adaptivity of SEURAT is desirable to solve the propagation of \Ly\ \ensuremathα photons in the interstellar medium of young star-forming galaxies like \Ly\ \ensuremathα emitters (LAEs). Thus, SEURAT provides a powerful tool to model the emergent spectra of \Ly\ \ensuremathα emission, which can be compared to the observations of LAEs.