For a multi-user multi-cell network, which suffers both intra-cell and inter-cell interference, this letter considers improper Gaussian signaling (IGS) as a means to improve the achievable rate. The problem of interest is designing of improper Gaussian signals' augmented covariance matrices to maximize the users' minimum rate subject to transmit power constraints. This problem is seen as a nonconvex matrix optimization problem, which cannot be solved by conventional techniques, such as weighted minimum mean square error minimization or alternating optimization. A path-following algorithm, which iterates a sequence of improved feasible points, is proposed for its computation. The provided simulation results for three cells serving 18 users show that IGS offers a much better max-min rate compared with that achieved by conventional proper Gaussian signaling. Another problem of maximizing the energy efficiency in IGS is also considered.