We achieve a compact optical frequency standard with an extended cavity diode laser locked to the 459 nm 6S 1/2 -7P 1/2 transition of thermal 133 Cs atoms in a φ 10 mm × 50 mm glass cell, using modulation transfer spectroscopy (MTS). The self-estimated frequency stability of this laser is 1.4 × 10 −14 / √ τ . With heterodyne measurement, we verify the linewidth-narrowing effect of MTS locking and measure the frequency stability of the locked laser. The linewidth of each laser is reduced from the free-running 69.6 kHz to 10.3 kHz after MTS stabilization, by a factor of 6.75. The Allan deviation measured via beat detection is 2.1 × 10 −13 / √ τ for each MTS-stabilized laser. In addition, we measure the hyperfine structure of the 7P 1/2 energy level based on the heterodyne measurements, and calculate the magnetic dipole constant A of the Cs 7P 1/2 level to be 94.38(6) MHz, which agrees well with previous measurements. This compact optical frequency standard can also be used in other applications that require high-stability lasers, such as laser interferometry, laser cooling, geodesy, and so on.