A new kind of left-handed material (LHM) is designed using series LC resonance elements (SLCREs) as doped isomerization units that are inserted into the LHMs. The new LHMs are called SLCDLHMs, in which the doping effects are numerically studied through the transmission spectra of plane electromagnetic waves by using both the finite-difference time-domain (FDTD) method and CST microwave studio software. In the lower frequency range a new pass band is presented, which could be tuned from 1.5 GHz to 6.5 GHz by varying the numerical values of the capacitance and inductance of the SLCREs. More interesting, when the numerical values of the capacitors or inductors of the SLCREs are adjusted, it could attenuate, shift, and expand the basic left-handed pass band of the SLCDLHMs. Consequently, a kind of quantitatively controllable SLCDLHMs could be designed to meet the need of the desired transmission properties by varying the LC parameters of the SLCREs.