The currently available β-lactamase inhibitors are insufficient to inhibit the incessantly increasing β-lactamase, and novel β-lactamase inhibitors has been required today for the difficult treatment for bacterial infectious diseases caused by resistant bacteria which produce class C β-lactamase, extended-spectrum β-lactamase (ESBL) belonging to class A and D, or class A KPC-2 decomposing even carbapenem as a last resort for β-lactam antibiotic.A compound represented by the the formula (I), preparation process of the same, β-lactamase inhibitors and method for treating bacterial infectious diseases are provided.