We have constructed a narrow-linewidth single-longitudinal-mode unidirectional $Er^{3+}$ -doped fiber laser using a fiber Bragg grating incorporated by a three port optical circulator with a compact configuration. Using a conventional delayed self-heterodyne detection technique with Mach-Zehnder interferometer a linewidth of 5 kHz was measured. In a single-longitudinal-mode operation, output power of up to 2.7 mW at 1548 nm were obtained for a launched pump power of 43 mW at 980 nm.