In a lithium-ion battery energy storage system for electromagnetic launch, the accurate extraction of the battery pack stray inductance is significant for designing a reasonable system solution. To meet this demand, the process of battery pack pulse discharge was modeled and analyzed, and the discharge stage suitable for stray inductance extraction was obtained. The method of solving the numerical differentiation by discrete Fourier transform was changed to the sliding-window recursive form, which was combined with multi-innovation least square algorithm, so a novel stray inductance extraction method was proposed, which can make full use of waveform data. Experimental results show that this method can extract stray inductance more accurately and reliably than the traditional method, and the calculation results are consistent under different discharge currents.