We have measured low-temperature specific heat C(T, H) of La 1.9 Sr 0.1 Cu 1-x Zn x O 4 (x=0, 0.01, and 0.02) both in zero and applied magnetic fields. A pronounced dip of C/T below 2 K was first observed in Zn-doped samples, which is absent in the nominally clean one. If the origin of the dip in C/T is electronic, the quasiparticle density of states N(E) in Zn-doped samples may be depressed below a small energy scale E 0 . The present data can be well described by the model N(E)=N(0)+aE 1/2 , with a non-zero N(0) and positive a. N(E) is argued to vanish as E or E 2 depending on whether the time reversal is a good symmetry or not.In principle, the low-temperature specific heat (LTSH) C(T) is a powerful probe of N(E) of the quasiparticle low energy excitation. Nevertheless, previous LTSH experiments in impurity-doped (especially Zn-doped) [14,15,20] cuprates usually suffered a upturn in C/T at low temperatures. This upturn hinders the investigation of the low-temperature electronic contribution in C, and is presumably due to either a hyperfine contribution or the local magnetic moment both of which probably are associated with defects in samples.To shed light on the issue of the low-energy quasiparticle N(E), we have carefully prepared Zn-and Ni-doped La 1.9 Sr 0.1 CuO 4 . These samples show no upturn in C/T down to the lowest experiment temperature 0.6 K. Therefore, LTSH can be readily used to probe N(E) and provide