A Coriolis mass flow measuring device includes a vibratory measuring transducer having at least one measuring tube, which has medium flowing through it during operation. In operation, the measuring tube is caused by an exciter arrangement to undergo mechanical oscillations, especially bending oscillations. Additionally, the Coriolis mass flow measuring device includes a sensor arrangement for producing oscillation measurement signals (s1, S2) representing the inlet-end and outlet-end oscillations of the measuring tube. Measuring device electronics controlling the exciter arrangement produces an exciter current (iexc) and an intermediate value (X′m) derived from the oscillation measurement signals (s1, s2). This intermediate value represents an uncorrected mass flow. Derived from the exciter current and/or from a component of the exciter current (iexc), an intermediate value (X2) is produced, which corresponds to a damping of the oscillations of the measuring tube. This damping is especially a function of an apparent viscosity, and/or a viscosity-density product, of the medium guided in the measuring tube. Furthermore, a correction value (XK) is produced for the intermediate value (X′m) utilizing the intermediate value (X2) and a viscosity measurement value (Xη) determined initially or during operation. The viscosity measurement value (Xη) corresponds to a viscosity of the medium guided in the measuring tube and/or to a predetermined reference viscosity. On the basis of the intermediate value (X′m) and the correction value (XK), the measuring device electronics then produces an exact mass flow rate measurement value (Xm).