The temperature ($T$) and magnetic field ($H$) dependence of the magnetic penetration depth, $lambda(T,H)$, in Ca(Al$_{0.5}$Si$_{0.5}$)$_2$ exhibits significant deviation from that expected for conventional BCS superconductors. In particular, it is inferred from a field dependence of $lambda(H)$ ($propto H$) at 2.0 K that the quasiparticle excitation is strongly enhanced by the Doppler shift. This suggests that the superconducting order parameter in Ca(Al$_{0.5}$Si$_{0.5}$)$_2$ is characterized by a small energy scale $Delta_S/k_Ble 2$ K originating either from anisotropy or multi-gap structure.