We present ground-based high-resolution high S/N spectra of the slowly pulsating B star HD 147394. Two frequencies are clearly found in the moments of the Si II 4128-4130 doublet: f(1) = 0.8008 c d(-1) and f(2) = 0.7813 c d(-1). The frequency f(1) is also found in the HIPPARCOS data. A third frequency is also present in our spectroscopic data: f(3) = 0.7175 c d(-1) or its aliases due to the time sampling. A mode identification is performed by means of a new version of the moment method optimized for multiperiodic signals. It points towards several equivalent solutions of non-axisymmetric l less than or equal to 3 for all three modes. We have too limited information to perform seismic modelling at this stage, but we do show that the different possibilities for the mode identifications are compatible with pulsational models for SPBs.