The Long Term Evolution (LTE) system is based on the Orthogonal Frequency Division Multiplexing (OFDM) and relies its channel estimation on the lattice-type pilot samples in the multipath fading channel environment. The estimation of the channel frequency response (CFR) makes use of the least squares estimate (LSE) for each pilot samples, followed by an interpolation both in time- and in frequency-domain to fill up the channel estimates for subcarriers corresponding to data samples. Any interpolation scheme could be adopted for this purpose. Depending on the requirements of the target system, we may choose a simple linear interpolation or a sophisticated one. For any choice of an interpolation scheme, these is a trade-off between estimation accuracy and numerical cost. For those wireless communication systems based on the OFDM and the preamble-type pilot structure, the DFT-based channel estimation and its variants have been successfully. Yet, it may not be suitable for the lattice-type pilot structure, since the pilot samples are not sufficient to provide an accurate estimate and it is known to be sensitive to the location as well as the length of the time-domain window. In this paper, we propose a simple interpolated based on the upsampling mechanism in the multirate signal processing. The proposed method provides an excellent alternative to the DFT-based methods in terms of numerical cost and accuracy. The performance of the proposed technique is verified on a multipath environment suggested on a 3GPP LTE specification.