The quantitative measurement of plasma soft x-ray spectra is an important diagnostic problem in indirect-drive laser inertial confinement fusion (ICF). We designed, built, and tested a compact multichannel soft x-ray spectrometer with both spatial and temporal resolution capabilities for the detection of the spatiotemporal distribution of soft x-ray spectra. The spectrometer occupies a small solid angle, and the close measurement angle used for each channel enables the measurement of the angular distribution of emitting soft x-rays in ICF experiments. The spectrometer comprises pinhole, filter, and multilayer flat mirror arrays, and an x-ray streak camera. Its energy range is 0.1 - 3 keV. The dispersive elements of the spectrometer were calibrated at the Beijing Synchrotron Radiation Facility. The accuracy of the calibration was ≤ 5%, and the combined energy resolution (E/ΔE) of the calibrated dispersive elements of each channel was higher than 10. Finally, the instrument was tested at the Shenguang-III Laser Facility. The measurement results of x-ray radiation flux are agreed well with the experimental results of the M-band flat-response x-ray diode, demonstrating the feasibility of the proposed spectrometer configuration.