Conventionally, a substantial number of reflecting elements (REs) is deployed at the intelligent reflecting surface (IRS) to mitigate the effect of the double-fading attenuation in the IRS-aided link, leading to a large surface size and considerable power consumption. In this paper, a new type of IRS, called active IRS, is proposed to solve this challenge by allowing each RE to amplify the incident signal with the assistance of the active loads (negative resistances). Thus, given a power budget at the IRS, the IRS-aided link can be enhanced by increasing the number of active REs as well as amplifying the incident signal. Specifically, we consider the use of an active IRS-aided single input multiple output (SIMO) system, in which the received signal-to-noise ratio (SNR) is maximized, by optimizing not only the reflecting coefficient matrix at the IRS but also the receive beamforming at the receiver. To solve this non-convex problem, we propose an alternating optimization algorithm, that iteratively optimizes the two design variables. In particular, the receive beamforming is founded to be in the form of a linear minimum mean square error (MMSE) detector, and the reflecting coefficient matrix is obtained via the Charnes-Cooper transformation and the semi-definite programming (SDP). Simulation results show that under a practical power consumption model, the proposed active IRS-aided system achieves better performance over the conventional passive IRS-aided system with the same power budget.