/ AbstractWe present the data-processing algorithms and the performance of CONCERTO (CarbON CII line in post-rEionisation and ReionisaTiOn epoch) in continuum by analysing the data from the commissioning and scientific observations. The beam pattern is characterized by an effective FWHM of 31.9 $\pm$ 0.6" and 34.4 $\pm$ 1.0" for high-frequency (HF) and low-frequency (LF) bands. The main beam is slightly elongated with a mean eccentricity of 0.46. Two error beams of $\sim$65" and $\sim$130" are characterized, enabling the estimate of a main beam efficiency of $\sim$0.52. The field of view is accurately reconstructed and presents coherent distortions between the HF and LF arrays. LEKID parameters were robustly determined for 80% of the read tones. Cross-talks between LEKIDs are the first cause of flagging, followed by an excess of eccentricity for $\sim$10% of the LEKIDs, all located in a given region of the field of view. On the 44 scans of Uranus selected for the absolute photometric calibration, 72.5% and 78.2% of the LEKIDs are selected as valid detectors with a probability >70%. By comparing Uranus measurements with a model, we obtain calibration factors of 19.5$\pm$0.6 [Hz/Jy] and 25.6$\pm$0.9 [Hz/Jy] for HF and LF. The point-source continuum measurement uncertainties are 3.0% and 3.4% for HF and LF bands. The RMS of CONCERTO maps is verified to evolve as proportional to the inverse square root of integration time. The measured NEFDs for HF and LF are 115$\pm$2 mJy/beam$\cdot$s$^{1/2}$ and 95$\pm$1 mJy/beam$\cdot$s$^{1/2}$, obtained using CONCERTO data on the COSMOS field for a mean precipitable water vapour and elevation of 0.81 mm and 55.7 deg. CONCERTO demonstrates unique capabilities in fast dual-band spectral mapping with a $\sim$18.5' instantaneous field-of-view. CONCERTO's performance in continuum is perfectly in line with expectations.