We report on single-crystal growths of the SrTb$_2$O$_4$ compound by a super-necking technique with a laser-floating-zone furnace and study the stoichiometry, growth mode, and structural and magnetic properties by scanning electronic microscopy, neutron Laue, X-ray powder diffraction, and the physical property measurement system. We optimized the growth parameters, mainly the growth speed, atmosphere, and the addition of a Tb$_4$O$_7$ raw material. Neutron Laue diffraction displays the characteristic feature of a single crystal. Our study reveals an atomic ratio of Sr{:}Tb $ = 0.97(2){:}2.00(1)$ and a possible layer by layer crystal growth mode. Our X-ray powder diffraction study determines the crystal structure, lattice constants and atomic positions. The paramagnetic (PM) Curie{--}Weiss (CW) temperature $\theta_{\texttt{CW}} =$ 5.00(4) K, and the effective PM moment $M^{\texttt{eff}}_{\texttt{mea}} =$ 10.97(1) $\mu_\texttt{B}$ per Tb$^{3+}$ ion. The data of magnetization versus temperature can be divided into three regimes, showing a coexistence of antiferromagnetic and ferromagnetic interactions. This probably leads to the magnetic frustration in the SrTb$_2$O$_4$ compound. The magnetization at 2 K and 14 T originates from both the Tb1 and Tb2 sites and is strongly frustrated with an expected saturation field at $\sim$41.5 T, displaying an intricate phase diagram with three ranges.