Precise controlling of current produced by power converters is an important topic that has attracted interests over the last few decades. With the recent proliferation of grid-tied converters where the control of power flow is indirectly governed by the accuracy of current tracking, motivation to develop dynamically fast and accurate current controllers is even more intensive with more features expected to be embedded within a single control module. Believing in its continual importance, this paper contributes by proposing a complex-vector time-delay control scheme that can achieve high tracking precision and disturbance rejection. In principle, the proposed scheme can either be implemented solely in the stationary frame or in a "mixed" stationary and synchronous frame, termed as mixed frame in the paper. Regardless of the frame orientation chosen, the scheme always exhibits ease of implementation since only a small amount of memory space for storing time-delayed values and simple arithmetic computations are needed for its physical realization. In addition to that, other advantages of the scheme include its abilities to compensate for negative-sequence, load and grid harmonic components using a set of load-matching control characteristics that are less sensitive to external noise interferences. These added features, complementing the basic requirement of fast and accurate fundamental positive-sequence tracking, render the proposed scheme as an attractive alternative for high-end converter control. Lastly, for proving its practicality, experimental testing of the scheme Is performed digitally using a commercial grid converter with some informative results captured and compared with those of an existing scheme.