In this paper, we present SMKA18 analysis, which is a first attempt to extract the set of next-to-next-leading-order (NNLO) spin-dependent parton distribution functions (spin-dependent PDFs) and their uncertainties determined through the Laplace transform technique and Jacobi polynomial approach. Using the Laplace transformations, we present an analytical solution for the spin-dependent Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations at NNLO approximation. The results are extracted using a wide range of proton gp1(x,Q2), neutron g n1(x,Q2) , and deuteron gd1(x,Q2) spin-dependent structure functions data set including the most recent high-precision measurements from COMPASS16 experiments at CERN, which are playing an increasingly important role in global spin-dependent fits. The careful estimations of uncertainties have been done using the standard Hessian error propagation. We will compare our results with the available spin-dependent inclusive deep inelastic scattering data set and other results for the spin-dependent PDFs in the literature. The results obtained for the spin-dependent PDFs as well as spin-dependent structure functions are clearly explained both in the small and large values of x.