  It is challenged only recently that the precision attainable in any
measurement of a physical parameter is fundamentally limited by the quantum
Cram\'{e}r-Rao Bound (QCRB). Here, targeting at measuring parameters in
strongly dissipative systems, we propose an innovative measurement scheme
called {\it dissipative adiabatic measurement} and theoretically show that it
can beat the QCRB. Unlike projective measurements, our measurement scheme,
though consuming more time, does not collapse the measured state and, more
importantly, yields the expectation value of an observable as its measurement
outcome, which is directly connected to the parameter of interest. Such a
direct connection {allows to extract} the value of the parameter from the
measurement outcomes in a straightforward manner, with no fundamental
limitation on precision in principle. Our findings not only provide a marked
insight into quantum metrology but also are highly useful in dissipative
quantum information processing.
