Education is a key to a successful life for all human beings. Having a good education certainly helps people to have a better life and improve their living standard. Therefore, education should be continually conducted meaningfully to enhance students’ competence. However, carrying out effective learning and appropriate classroom assessment during the coronavirus pandemic could be highly challenging for the teachers to do. Teachers need to utilize various technological devices to assess students' learning competence. This is due to online learning has become a priority in learning activities in the pandemic situation. Consequently, teachers must have broader horizons on how to conduct the learning processes and appropriate assessment strategies and operate various communication technologies. This study found that English teachers implemented three types of online assessment strategies to improve students' learning competence during the pandemic of Covid-19 in Indonesia. Those strategies are online test administration, portfolio, and self-assessment. Several challenges were accoutered by the teachers in carrying out the classroom assessment through online systems such as slow internet network, expensive internet quota prices, limited access to computer and smartphone devices, poor ability in using digital technology, difficulty in conducting effective interaction. Feedback was occasionally provided when the learning processes were conducted through zoom meeting or google meet. The study implies that teachers should improve their communication technology ability and fulfill online assessment strategies' administrative procedures.