Vector orthogonal frequency division multiplexing (V-OFDM) is a general system that builds a bridge between OFDM and single-carrier frequency domain equalization in terms of intersymbol interference and receiver complexity. In this paper, we investigate the sparse multipath channel estimation and decoding for broadband V-OFDM systems. Unlike the non-sparse channel estimation, sparse channel estimation only needs to recover the nonzero taps with reduced complexity. Consider the pilot signals are transmitted through a sparse channel that has only a few nonzero taps with and without additive white Gaussian noise, respectively. The exactly and approximately sparse inverse fast Fourier transform (SIFFT) can be employed for these two cases. The SIFFT-based algorithm recovers the nonzero channel coefficients and their corresponding coordinates directly, which is significant to the proposed partial intersection sphere (PIS) decoding approach. Unlike the maximum likelihood (ML) decoding that enumerates symbol constellation and estimates the transmitted symbols with the minimum distance, the PIS decoding first generates the set of possible transmitted symbols and then chooses the transmitted symbols only from this set with the minimum distance. The diversity order of the PIS decoding is determined by not only the number of nonzero taps, but also the coordinates of nonzero taps, and the bit error rate (BER) is also influenced by vector block size to some extent but roughly independent of the maximum time delay. Simulation results indicate that by choosing appropriate sphere radius, the BER performance of the PIS decoding outperforms the conventional zero-forcing decoding and minimum mean square error decoding, and approximates to the ML decoding with the increase of signal-to-noise ratio, but reduces the computational complexity significantly.