An engine comprising: an engine body equipped with a supercharger; an engine rotational speed detection means which detects engine rotational speed (Ne); an engine load detection means which detects load (Ac) on the engine; a supercharging pressure detection means which detects supercharging pressure (Pb); a supercharger rotational speed detection means which detects supercharger rotational speed (Nc); and a control means which performs post-injection control at least once in expansion or exhaust stroke so as to increase exhaust energy, wherein the control means recognizes the engine rotational speed (Ne), the supercharging pressure (Pb), the load (Ac) on the engine, and the supercharger rotational speed (Nc), and performs the post-injection control so as to make the supercharger rotational speed (Nc) equal to target supercharger rotational speed (Ncm) calculated by the control means, the target supercharger rotational speed (Ncm) is set on a target supercharger rotational speed map (f4c(Ne,Pb,QM,Ncm)) being a four-dimensional map showing correlation of the engine rotational speed Ne, boost pressure Pb, main injection amount QM and turbo rotational speed Nc, by setting each target turbo rotational speed Ncm in the target supercharger rotational speed map (f4c (Ne, Pb, Qm, Ncm)) so as to minimize total amount of smoke, CO and HC in exhaust gas, and the control means judges whether absolute value of difference between the supercharger rotational speed (Nc) and the target supercharger rotational speed (Ncm) is smaller than a threshold (ΔNc) or not, and finishes the post-injection control and performs the normal operation when the absolute value is smaller than the threshold (ΔNc), and regulates the number of times of the injection and injection amount when the absolute value is not smaller than the threshold (ΔNc) so as to make the absolute value of difference between the supercharger rotational speed and the target supercharger rotational speed smaller than the threshold (ΔNc). an engine body equipped with a supercharger; an engine rotational speed detection means which detects engine rotational speed (Ne); an engine load detection means which detects load (Ac) on the engine; a supercharging pressure detection means which detects supercharging pressure (Pb); a supercharger rotational speed detection means which detects supercharger rotational speed (Nc); and a control means which performs post-injection control at least once in expansion or exhaust stroke so as to increase exhaust energy, wherein the control means recognizes the engine rotational speed (Ne), the supercharging pressure (Pb), the load (Ac) on the engine, and the supercharger rotational speed (Nc), and performs the post-injection control so as to make the supercharger rotational speed (Nc) equal to target supercharger rotational speed (Ncm) calculated by the control means, the target supercharger rotational speed (Ncm) is set on a target supercharger rotational speed map (f4c(Ne,Pb,QM,Ncm)) being a four-dimensional map showing correlation of the engine rotational speed Ne, boost pressure Pb, main injection amount QM and turbo rotational speed Nc, by setting each target turbo rotational speed Ncm in the target supercharger rotational speed map (f4c (Ne, Pb, Qm, Ncm)) so as to minimize total amount of smoke, CO and HC in exhaust gas, and the control means judges whether absolute value of difference between the supercharger rotational speed (Nc) and the target supercharger rotational speed (Ncm) is smaller than a threshold (ΔNc) or not, and finishes the post-injection control and performs the normal operation when the absolute value is smaller than the threshold (ΔNc), and regulates the number of times of the injection and injection amount when the absolute value is not smaller than the threshold (ΔNc) so as to make the absolute value of difference between the supercharger rotational speed and the target supercharger rotational speed smaller than the threshold (ΔNc).