Speech phase prediction, which is a significant research focus in the field of signal processing, aims to recover speech phase spectra from amplitude-related features. However, existing speech phase prediction methods are constrained to recovering phase spectra with short frame shifts, which are considerably smaller than the theoretical upper bound required for exact waveform reconstruction of short-time Fourier transform (STFT). To tackle this issue, we present a novel long-frame-shift neural speech phase prediction (LFS-NSPP) method which enables precise prediction of long-frame-shift phase spectra from long-frame-shift log amplitude spectra. The proposed method consists of three stages: interpolation, prediction and decimation. The short-frame-shift log amplitude spectra are first constructed from long-frame-shift ones through frequency-by-frequency interpolation to enhance the spectral continuity, and then employed to predict short-frame-shift phase spectra using an NSPP model, thereby compensating for interpolation errors. Ultimately, the long-frame-shift phase spectra are obtained from short-frame-shift ones through frame-by-frame decimation. Experimental results show that the proposed LFS-NSPP method can yield superior quality in predicting long-frame-shift phase spectra than the original NSPP model and other signal-processing-based phase estimation algorithms.