Amorphous $BaTi_4O_9$ ($BT_4$) film was deposited on Pt/Si substrate by RF magnetron sputter and their dielectric properties and electrical properties are investigated. A cross sectional SEM image and AFM image of the surface of the amorphous $BT_4$ film deposited at room temperature showed the film was grown well on the substrate. The amorphous $BT_4$ film had a large dielectric constant of 32, which is similar to that of the crystalline $BT_4$ film. The leakage current density of the $BT_4$ film was low and a Poole-Frenkel emission was suggested as the leakage current mechanism. A positive quadratic voltage coefficient of capacitance (VCC) was obtained for the $BT_4$ film with a thickness of <70 nm and it could be due to the free carrier relaxation. However, a negative quadratic VCC was obtained for the films with a thickness ${geq}96nm$, possibly due to the dipolar relaxation. The 55 nm-thick $BT_4$ film had a high capacitance density of $5.1fF/{mu}m^2$ with a low leakage current density of $11.6nA/cm^2$ at 2 V. Its quadratic and linear VCCs were $244ppm/V^2$ and -52 ppm/V, respectively, with a low temperature coefficient of capacitance of $961ppm/^{circ}C$ at 100 kHz. These results confirmed the potential suitability of the amorphous $BT_4$ film for use as a high performance metal-insulator-metal (MIM) capacitor.