The pseudospectral method is a highly accurate numerical scheme suitable for turbulence simulations. We have developed an open-source pseudospectral code, calliope, which adopts the P3DFFT library to perform a fast Fourier transform with the two-dimensional (pencil) decomposition of numerical grids. calliope can solve incompressible magnetohydrodynamics (MHD), isothermal compressible MHD, and rotational reduced MHD with parallel computation using very large numbers of cores (>105 cores for 20483 grids). The code can also solve for local magnetorotational turbulence in a shearing frame using the remapping method. calliope is currently the only pseudospectral code that can compute magnetorotational turbulence using pencil-domain decomposition. This paper presents the numerical scheme of calliope and the results of linear and nonlinear numerical tests, including compressible local magnetorotational turbulence with the largest grid number reported to date.