We report measurements of London penetration depth λ(T ) for the noncentrosymmetric superconductor BiPd by using a tunnel diode oscillator. Pronounced anisotropic behavior is observed in the low-temperature penetration depth; the in-plane penetration depth λac(T ) follows an exponential decrease, but the interplane penetration depth λ b (T ) shows power-law-type behavior. The superfluid density ρs(T ), converted from the penetration depth λ(T ), is best fitted by an anisotropic two-band BCS model. We argue that such a complex order parameter is attributed to the admixture of spin-singlet and spin-triplet pairing states as a result of antisymmetric spin-orbit coupling in BiPd.Considerable attention has been devoted to the study of noncentrosymmetric (NCS) superconductors (SCs) and their exotic properties in recent years. 1 The absence of an inversion symmetry introduces an asymmetric potential gradient and, therefore, yields an antisymmetric spin-orbit coupling (ASOC). The ASOC may split the electron bands by lifting the spin degeneracy, allowing admixture of spin-singlet and spin-triplet pairing states within the same orbital channel. 2 Furthermore, it was recently proposed that NCS SCs with a strong SOC are potential candidates for realizing topological superconductivity. 3 Currently, the effect of broken inversion symmetry on superconductivity remains a puzzle and the role of ASOC on the superconducting pairing state is still highly controversial. 4 Unconventional superconductivity was observed in the heavy fermion superconductors CePt 3 Si, 5,6 CeRhSi 3 , 7 and CeIrSi 3 , 8 as well as in Li 2 Pt 3 B. 9 On the other hand, BCS-like superconductivity was claimed in a number of weakly correlated NCS SCs with heavy atoms, e.g., Re 3 W, 10 Mg 10 Ir 19 B 16 , 11 BaPtSi 3 12 and Nb x Re 1−x . 13 The determinant parameter remains to be revealed for the pairing states of NCS SCs. Theoretically, multiband superconductivity with anisotropic gaps or even a nodal gap structure is expected for NCS SCs, in particular when the band splitting E ASOC becomes comparable or even larger than the superconducting gap. 2 To reveal the anisotropic gap structure in NCS SCs, high-quality single crystals are necessary. Unfortunately, most of the previous measurements were performed on polycrystalline samples, which restricted our studies on their complex gap symmetry.Recently, a new noncentrosymmetric superconductor, BiPd, was successfully synthesized. 14 This compound undergoes a structural transition from β-BiPd (orthorhombic,Cmc2 1 ) to α-BiPd (monoclinic, P2 1 ) at 210 • C and then becomes superconducting at T c ≃ 3.7K. 14 In comparison with many other NCS SCs, BiPd is a weakly correlated compound possessing a heavy atom Bi. Furthermore, the sample quality for BiPd is much higher than many other NCS SCs investigated to date. These unique characteristics provide us with a great opportunity to study the exotic pairing state of NCS SCs. Measurements of point contact Andreev reflection (PCAR) spectra showed evidence of multiple supercondu...