A peaky filter comprises a covering and a corresponding base, a supporting frame connected between the covering and the base, and a multifold filter covering the exterior of the supporting frame. The supporting frame includes plural transversely spaced first supports and plural connectors. Each support has a supporting rod and a plurality of longitudinally spaced supporting members connected to the supporting rod. Each supporting member has a first supporting leg and a second supporting leg extending radially and outwardly from the supporting rod. Each connector has a first connecting part and a second connecting part, which are used for respectively connecting one end of the first supporting leg of one support and one end of the second supporting leg of another adjacent support to connect elastically the plurality of transversely spaced supports, and consequently alter the size of the supporting frame and the filtering area of the filter.