Recently, a signature of high-temperature superconductivity above the liquid nitrogen temperature (77 K) was reported for La3Ni2O7−δ under pressure. This finding immediately stimulated intense interest in the possible mechanism of high-Tc superconductivity in double-layer nickelates. Notably, the pressure-dependent phase diagram inferred from transport measurements indicates that the superconductivity under high pressure emerges from the suppression of density-wave-like order at ambient pressure, which is similar to high-temperature superconductors. Therefore, clarifying the exact nature of the density-wave-like transition is important for determining the superconducting mechanism in double-layer nickelates. Here, nuclear magnetic resonance (NMR) spectroscopy of 139La nuclei was performed to study the density-wave-like transition in a single crystal of La3Ni2O7−δ. At high temperatures, two sets of sharp 139La NMR peaks are clearly distinguishable from a broad background signals, which are ascribed to La(1) sites from two bilayer Ruddlesden-Popper phases with different oxygen vacancy δ. As the temperature decreases, the temperature-dependent 139La NMR spectra and nuclear spin-lattice relaxation rate (1/T1) for both La(1) sites provide evidence of spin-density-wave (SDW) ordering below the transition temperature (TSDW), which is approximately 150 K. The anisotropic splitting in the NMR spectra suggests the formation of a possible double spin stripe with magnetic moments aligned along the c-axis. Furthermore, we studied the pressure-dependent SDW transition up to ∼ 2.7 GPa. Surprisingly, the TSDW inferred from NMR measurements of both La(1) sites increases with increasing pressure, which is opposite to the results from previous transport measurements under pressure and suggests an intriguing phase diagram between superconductivity and SDW. In contrast, the present 139La NMR is insensitive to the possible charge-density-wave (CDW) order in the Ni-O planes. All these results will be helpful for building a connection between superconductivity and magnetic interactions in double-layer nickelates.