This paper considers the joint antenna selection (AS) problem for a classical two-user non-orthogonal multiple access (NOMA) network where both the base station and users are equipped with multiple antennas. Since the exhaustive-search-based optimal AS scheme is computationally prohibitive when the number of antennas is large, two computationally efficient joint AS algorithms, namely max-min-max AS (AIA-AS) and max-max-max AS (A$^3$-AS), are proposed to maximize the system sum-rate. The asymptotic closed-form expressions for the average sum-rates for both AIA-AS and A$^3$-AS are derived in the high signal-to-noise ratio (SNR) regime, respectively. Numerical results demonstrate that both AIA-AS and A$^3$-AS can yield significant performance gains over comparable schemes. Furthermore, AIA-AS can provide better user fairness, while the A$^3$-AS scheme can achieve the near-optimal sum-rate performance.